--- _id: '2700' alternative_title: - Quantum Theory from Small to Large Scales author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 citation: ama: 'Erdös L. Lecture notes on quantum Brownian motion. In: Vol 95. Oxford University Press; 2012:3-98.' apa: Erdös, L. (2012). Lecture notes on quantum Brownian motion (Vol. 95, pp. 3–98). Presented at the Les Houches Summer School 2010, Oxford University Press. chicago: Erdös, László. “Lecture Notes on Quantum Brownian Motion,” 95:3–98. Oxford University Press, 2012. ieee: L. Erdös, “Lecture notes on quantum Brownian motion,” presented at the Les Houches Summer School 2010, 2012, vol. 95, pp. 3–98. ista: Erdös L. 2012. Lecture notes on quantum Brownian motion. Les Houches Summer School 2010, Quantum Theory from Small to Large Scales, vol. 95, 3–98. mla: Erdös, László. Lecture Notes on Quantum Brownian Motion. Vol. 95, Oxford University Press, 2012, pp. 3–98. short: L. Erdös, in:, Oxford University Press, 2012, pp. 3–98. conference: name: Les Houches Summer School 2010 date_created: 2018-12-11T11:59:08Z date_published: 2012-05-24T00:00:00Z date_updated: 2021-01-12T06:59:08Z day: '24' extern: 1 intvolume: ' 95' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1009.0843 month: '05' oa: 1 page: 3 - 98 publication_status: published publisher: Oxford University Press publist_id: '4196' quality_controlled: 0 status: public title: Lecture notes on quantum Brownian motion type: conference volume: 95 year: '2012' ... --- _id: '2715' abstract: - lang: eng text: 'We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning vertices from where the objective can be ensured with probability 1. We study for the first time the average case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average case running time is linear (as compared to the worst case linear number of iterations and quadratic time complexity). Second, for the average case analysis over all MDPs we show that the expected number of iterations is constant and the average case running time is linear (again as compared to the worst case linear number of iterations and quadratic time complexity). Finally we also show that given that all MDPs are equally likely, the probability that the classical algorithm requires more than constant number of iterations is exponentially small.' alternative_title: - LIPIcs author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Manas full_name: Joglekar, Manas last_name: Joglekar - first_name: Nisarg full_name: Shah, Nisarg last_name: Shah citation: ama: 'Chatterjee K, Joglekar M, Shah N. Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives. In: Vol 18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2012:461-473. doi:10.4230/LIPIcs.FSTTCS.2012.461' apa: 'Chatterjee, K., Joglekar, M., & Shah, N. (2012). Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives (Vol. 18, pp. 461–473). Presented at the FSTTCS: Foundations of Software Technology and Theoretical Computer Science, Hyderabad, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2012.461' chicago: Chatterjee, Krishnendu, Manas Joglekar, and Nisarg Shah. “Average Case Analysis of the Classical Algorithm for Markov Decision Processes with Büchi Objectives,” 18:461–73. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012. https://doi.org/10.4230/LIPIcs.FSTTCS.2012.461. ieee: 'K. Chatterjee, M. Joglekar, and N. Shah, “Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives,” presented at the FSTTCS: Foundations of Software Technology and Theoretical Computer Science, Hyderabad, India, 2012, vol. 18, pp. 461–473.' ista: 'Chatterjee K, Joglekar M, Shah N. 2012. Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives. FSTTCS: Foundations of Software Technology and Theoretical Computer Science, LIPIcs, vol. 18, 461–473.' mla: Chatterjee, Krishnendu, et al. Average Case Analysis of the Classical Algorithm for Markov Decision Processes with Büchi Objectives. Vol. 18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 461–73, doi:10.4230/LIPIcs.FSTTCS.2012.461. short: K. Chatterjee, M. Joglekar, N. Shah, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 461–473. conference: end_date: 2012-12-17 location: Hyderabad, India name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science' start_date: 2012-12-15 date_created: 2018-12-11T11:59:13Z date_published: 2012-12-10T00:00:00Z date_updated: 2023-02-23T10:06:04Z day: '10' ddc: - '000' department: - _id: KrCh doi: 10.4230/LIPIcs.FSTTCS.2012.461 ec_funded: 1 file: - access_level: open_access checksum: d4d644ed1a885dbfc4fa1ef4c5724dab content_type: application/pdf creator: system date_created: 2018-12-12T10:13:53Z date_updated: 2020-07-14T12:45:45Z file_id: '5040' file_name: IST-2016-525-v1+1_42_1_.pdf file_size: 519040 relation: main_file file_date_updated: 2020-07-14T12:45:45Z has_accepted_license: '1' intvolume: ' 18' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '12' oa: 1 oa_version: Published Version page: 461 - 473 project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2587B514-B435-11E9-9278-68D0E5697425 name: Microsoft Research Faculty Fellowship publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '4180' pubrep_id: '525' quality_controlled: '1' related_material: record: - id: '1598' relation: later_version status: public scopus_import: 1 status: public title: Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 18 year: '2012' ... --- _id: '10904' abstract: - lang: eng text: Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω-regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on VASS (vector addition systems with states). Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts. acknowledgement: 'Author supported by Austrian Science Fund (FWF) Grant No P 23499-N23, FWF NFN Grant No S11407 (RiSE), ERC Start Grant (279307: Graph Games), Microsoft faculty fellowship.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Mickael full_name: Randour, Mickael last_name: Randour - first_name: Jean-François full_name: Raskin, Jean-François last_name: Raskin citation: ama: 'Chatterjee K, Randour M, Raskin J-F. Strategy synthesis for multi-dimensional quantitative objectives. In: Koutny M, Ulidowski I, eds. CONCUR 2012 - Concurrency Theory. Vol 7454. Berlin, Heidelberg: Springer; 2012:115-131. doi:10.1007/978-3-642-32940-1_10' apa: 'Chatterjee, K., Randour, M., & Raskin, J.-F. (2012). Strategy synthesis for multi-dimensional quantitative objectives. In M. Koutny & I. Ulidowski (Eds.), CONCUR 2012 - Concurrency Theory (Vol. 7454, pp. 115–131). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642-32940-1_10' chicago: 'Chatterjee, Krishnendu, Mickael Randour, and Jean-François Raskin. “Strategy Synthesis for Multi-Dimensional Quantitative Objectives.” In CONCUR 2012 - Concurrency Theory, edited by Maciej Koutny and Irek Ulidowski, 7454:115–31. Berlin, Heidelberg: Springer, 2012. https://doi.org/10.1007/978-3-642-32940-1_10.' ieee: K. Chatterjee, M. Randour, and J.-F. Raskin, “Strategy synthesis for multi-dimensional quantitative objectives,” in CONCUR 2012 - Concurrency Theory, Newcastle upon Tyne, United Kingdom, 2012, vol. 7454, pp. 115–131. ista: 'Chatterjee K, Randour M, Raskin J-F. 2012. Strategy synthesis for multi-dimensional quantitative objectives. CONCUR 2012 - Concurrency Theory. CONCUR: Conference on Concurrency Theory, LNCS, vol. 7454, 115–131.' mla: Chatterjee, Krishnendu, et al. “Strategy Synthesis for Multi-Dimensional Quantitative Objectives.” CONCUR 2012 - Concurrency Theory, edited by Maciej Koutny and Irek Ulidowski, vol. 7454, Springer, 2012, pp. 115–31, doi:10.1007/978-3-642-32940-1_10. short: K. Chatterjee, M. Randour, J.-F. Raskin, in:, M. Koutny, I. Ulidowski (Eds.), CONCUR 2012 - Concurrency Theory, Springer, Berlin, Heidelberg, 2012, pp. 115–131. conference: end_date: 2012-09-07 location: Newcastle upon Tyne, United Kingdom name: 'CONCUR: Conference on Concurrency Theory' start_date: 2012-09-04 date_created: 2022-03-21T08:00:21Z date_published: 2012-09-15T00:00:00Z date_updated: 2023-02-23T10:55:06Z day: '15' department: - _id: KrCh doi: 10.1007/978-3-642-32940-1_10 ec_funded: 1 editor: - first_name: Maciej full_name: Koutny, Maciej last_name: Koutny - first_name: Irek full_name: Ulidowski, Irek last_name: Ulidowski external_id: arxiv: - '1201.5073' intvolume: ' 7454' language: - iso: eng month: '09' oa_version: Preprint page: 115-131 place: Berlin, Heidelberg project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2587B514-B435-11E9-9278-68D0E5697425 name: Microsoft Research Faculty Fellowship publication: CONCUR 2012 - Concurrency Theory publication_identifier: eisbn: - '9783642329401' isbn: - '9783642329395' issn: - 0302-9743 - 1611-3349 publication_status: published publisher: Springer quality_controlled: '1' related_material: record: - id: '2716' relation: later_version status: public scopus_import: '1' status: public title: Strategy synthesis for multi-dimensional quantitative objectives type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7454 year: '2012' ... --- _id: '2770' abstract: - lang: eng text: 'Consider N×N Hermitian or symmetric random matrices H with independent entries, where the distribution of the (i,j) matrix element is given by the probability measure vij with zero expectation and with variance σ ιj 2. We assume that the variances satisfy the normalization condition Σiσij2=1 for all j and that there is a positive constant c such that c≤Nσ ιj 2 ιc -1. We further assume that the probability distributions νij have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eigenvalue distribution of H is given by the Wigner semicircle law uniformly up to the edges of the spectrum with an error of order (Nη) -1 where η is the imaginary part of the spectral parameter in the Stieltjes transform. There are three corollaries to this strong local semicircle law: (1) Rigidity of eigenvalues: If γj=γj,N denotes the classical location of the j-th eigenvalue under the semicircle law ordered in increasing order, then the j-th eigenvalue λj is close to γj in the sense that for some positive constants C, c P{double-struck}(∃j:|λ j-γ j|≥(logN) CloglogN[min(j,N-j+1)] -1/3N -2/3)≤ C exp[-(logN) cloglogN] for N large enough. (2) The proof of Dyson''s conjecture (Dyson, 1962 [15]) which states that the time scale of the Dyson Brownian motion to reach local equilibrium is of order N -1 up to logarithmic corrections. (3) The edge universality holds in the sense that the probability distributions of the largest (and the smallest) eigenvalues of two generalized Wigner ensembles are the same in the large N limit provided that the second moments of the two ensembles are identical.' author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau - first_name: Jun full_name: Yin, Jun last_name: Yin citation: ama: Erdös L, Yau H, Yin J. Rigidity of eigenvalues of generalized Wigner matrices. Advances in Mathematics. 2012;229(3):1435-1515. doi:10.1016/j.aim.2011.12.010 apa: Erdös, L., Yau, H., & Yin, J. (2012). Rigidity of eigenvalues of generalized Wigner matrices. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2011.12.010 chicago: Erdös, László, Horng Yau, and Jun Yin. “Rigidity of Eigenvalues of Generalized Wigner Matrices.” Advances in Mathematics. Academic Press, 2012. https://doi.org/10.1016/j.aim.2011.12.010. ieee: L. Erdös, H. Yau, and J. Yin, “Rigidity of eigenvalues of generalized Wigner matrices,” Advances in Mathematics, vol. 229, no. 3. Academic Press, pp. 1435–1515, 2012. ista: Erdös L, Yau H, Yin J. 2012. Rigidity of eigenvalues of generalized Wigner matrices. Advances in Mathematics. 229(3), 1435–1515. mla: Erdös, László, et al. “Rigidity of Eigenvalues of Generalized Wigner Matrices.” Advances in Mathematics, vol. 229, no. 3, Academic Press, 2012, pp. 1435–515, doi:10.1016/j.aim.2011.12.010. short: L. Erdös, H. Yau, J. Yin, Advances in Mathematics 229 (2012) 1435–1515. date_created: 2018-12-11T11:59:30Z date_published: 2012-02-15T00:00:00Z date_updated: 2021-01-12T06:59:35Z day: '15' doi: 10.1016/j.aim.2011.12.010 extern: 1 intvolume: ' 229' issue: '3' month: '02' page: 1435 - 1515 publication: Advances in Mathematics publication_status: published publisher: Academic Press publist_id: '4120' quality_controlled: 0 status: public title: Rigidity of eigenvalues of generalized Wigner matrices type: journal_article volume: 229 year: '2012' ... --- _id: '2769' abstract: - lang: eng text: We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {X J} N j=1 are close to their classical location {y j} N j=1 determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/N, the necessary apriori estimate on the location of eigenvalues requires only to know that E|x j - γ j| 2 ≤ N-1-ε on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for sample covariance matrices. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau - first_name: Jun full_name: Yin, Jun last_name: Yin citation: ama: Erdös L, Schlein B, Yau H, Yin J. The local relaxation flow approach to universality of the local statistics for random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2012;48(1):1-46. doi:10.1214/10-AIHP388 apa: Erdös, L., Schlein, B., Yau, H., & Yin, J. (2012). The local relaxation flow approach to universality of the local statistics for random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/10-AIHP388 chicago: Erdös, László, Benjamin Schlein, Horng Yau, and Jun Yin. “The Local Relaxation Flow Approach to Universality of the Local Statistics for Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2012. https://doi.org/10.1214/10-AIHP388. ieee: L. Erdös, B. Schlein, H. Yau, and J. Yin, “The local relaxation flow approach to universality of the local statistics for random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 48, no. 1. Institute of Mathematical Statistics, pp. 1–46, 2012. ista: Erdös L, Schlein B, Yau H, Yin J. 2012. The local relaxation flow approach to universality of the local statistics for random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 48(1), 1–46. mla: Erdös, László, et al. “The Local Relaxation Flow Approach to Universality of the Local Statistics for Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 48, no. 1, Institute of Mathematical Statistics, 2012, pp. 1–46, doi:10.1214/10-AIHP388. short: L. Erdös, B. Schlein, H. Yau, J. Yin, Annales de l’institut Henri Poincare (B) Probability and Statistics 48 (2012) 1–46. date_created: 2018-12-11T11:59:30Z date_published: 2012-02-01T00:00:00Z date_updated: 2021-01-12T06:59:34Z day: '01' doi: 10.1214/10-AIHP388 extern: 1 intvolume: ' 48' issue: '1' month: '02' page: 1 - 46 publication: Annales de l'institut Henri Poincare (B) Probability and Statistics publication_status: published publisher: Institute of Mathematical Statistics publist_id: '4121' quality_controlled: 0 status: public title: The local relaxation flow approach to universality of the local statistics for random matrices type: journal_article volume: 48 year: '2012' ... --- _id: '2767' abstract: - lang: eng text: 'Consider N × N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure ν ij with a subexponential decay. Let σ ij 2 be the variance for the probability measure ν ij with the normalization property that Σ iσ i,j 2 = 1 for all j. Under essentially the only condition that c ≤ N σ ij 2 ≤ c -1 for some constant c > 0, we prove that, in the limit N → ∞, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth M the local semicircle law holds to the energy scale M -1. ' author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau - first_name: Jun full_name: Yin, Jun last_name: Yin citation: ama: Erdös L, Yau H, Yin J. Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. 2012;154(1-2):341-407. doi:10.1007/s00440-011-0390-3 apa: Erdös, L., Yau, H., & Yin, J. (2012). Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-011-0390-3 chicago: Erdös, László, Horng Yau, and Jun Yin. “Bulk Universality for Generalized Wigner Matrices.” Probability Theory and Related Fields. Springer, 2012. https://doi.org/10.1007/s00440-011-0390-3. ieee: L. Erdös, H. Yau, and J. Yin, “Bulk universality for generalized Wigner matrices,” Probability Theory and Related Fields, vol. 154, no. 1–2. Springer, pp. 341–407, 2012. ista: Erdös L, Yau H, Yin J. 2012. Bulk universality for generalized Wigner matrices. Probability Theory and Related Fields. 154(1–2), 341–407. mla: Erdös, László, et al. “Bulk Universality for Generalized Wigner Matrices.” Probability Theory and Related Fields, vol. 154, no. 1–2, Springer, 2012, pp. 341–407, doi:10.1007/s00440-011-0390-3. short: L. Erdös, H. Yau, J. Yin, Probability Theory and Related Fields 154 (2012) 341–407. date_created: 2018-12-11T11:59:29Z date_published: 2012-10-01T00:00:00Z date_updated: 2021-01-12T06:59:33Z day: '01' doi: 10.1007/s00440-011-0390-3 extern: 1 intvolume: ' 154' issue: 1-2 month: '10' page: 341 - 407 publication: Probability Theory and Related Fields publication_status: published publisher: Springer publist_id: '4123' quality_controlled: 0 status: public title: Bulk universality for generalized Wigner matrices type: journal_article volume: 154 year: '2012' ... --- _id: '2768' abstract: - lang: eng text: We consider a two dimensional magnetic Schrödinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i. e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: David full_name: Hasler, David G last_name: Hasler citation: ama: Erdös L, Hasler D. Wegner estimate and Anderson localization for random magnetic fields. Communications in Mathematical Physics. 2012;309(2):507-542. doi:10.1007/s00220-011-1373-z apa: Erdös, L., & Hasler, D. (2012). Wegner estimate and Anderson localization for random magnetic fields. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-011-1373-z chicago: Erdös, László, and David Hasler. “Wegner Estimate and Anderson Localization for Random Magnetic Fields.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-011-1373-z. ieee: L. Erdös and D. Hasler, “Wegner estimate and Anderson localization for random magnetic fields,” Communications in Mathematical Physics, vol. 309, no. 2. Springer, pp. 507–542, 2012. ista: Erdös L, Hasler D. 2012. Wegner estimate and Anderson localization for random magnetic fields. Communications in Mathematical Physics. 309(2), 507–542. mla: Erdös, László, and David Hasler. “Wegner Estimate and Anderson Localization for Random Magnetic Fields.” Communications in Mathematical Physics, vol. 309, no. 2, Springer, 2012, pp. 507–42, doi:10.1007/s00220-011-1373-z. short: L. Erdös, D. Hasler, Communications in Mathematical Physics 309 (2012) 507–542. date_created: 2018-12-11T11:59:30Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T06:59:34Z day: '01' doi: 10.1007/s00220-011-1373-z extern: 1 intvolume: ' 309' issue: '2' month: '01' page: 507 - 542 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4122' quality_controlled: 0 status: public title: Wegner estimate and Anderson localization for random magnetic fields type: journal_article volume: 309 year: '2012' ... --- _id: '2775' abstract: - lang: eng text: The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix ensemble. For invariant matrix models, the eigenvalue distributions are given by a log-gas with potential V and inverse temperature β = 1, 2, 4, corresponding to the orthogonal, unitary and symplectic ensembles. For β ∉ {1, 2, 4}, there is no natural random matrix ensemble behind this model, but the statistical physics interpretation of the log-gas is still valid for all β > 0. The universality conjecture for invariant ensembles asserts that the local eigenvalue statistics are independent of V. In this article, we review our recent solution to the universality conjecture for both invariant and non-invariant ensembles. We will also demonstrate that the local ergodicity of the Dyson Brownian motion is the intrinsic mechanism behind the universality. Furthermore, we review the solution of Dyson's conjecture on the local relaxation time of the Dyson Brownian motion. Related questions such as delocalization of eigenvectors and local version of Wigner's semicircle law will also be discussed. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau citation: ama: Erdös L, Yau H. Universality of local spectral statistics of random matrices. Bulletin of the American Mathematical Society. 2012;49(3):377-414. doi:10.1090/S0273-0979-2012-01372-1 apa: Erdös, L., & Yau, H. (2012). Universality of local spectral statistics of random matrices. Bulletin of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/S0273-0979-2012-01372-1 chicago: Erdös, László, and Horng Yau. “Universality of Local Spectral Statistics of Random Matrices.” Bulletin of the American Mathematical Society. American Mathematical Society, 2012. https://doi.org/10.1090/S0273-0979-2012-01372-1. ieee: L. Erdös and H. Yau, “Universality of local spectral statistics of random matrices,” Bulletin of the American Mathematical Society, vol. 49, no. 3. American Mathematical Society, pp. 377–414, 2012. ista: Erdös L, Yau H. 2012. Universality of local spectral statistics of random matrices. Bulletin of the American Mathematical Society. 49(3), 377–414. mla: Erdös, László, and Horng Yau. “Universality of Local Spectral Statistics of Random Matrices.” Bulletin of the American Mathematical Society, vol. 49, no. 3, American Mathematical Society, 2012, pp. 377–414, doi:10.1090/S0273-0979-2012-01372-1. short: L. Erdös, H. Yau, Bulletin of the American Mathematical Society 49 (2012) 377–414. date_created: 2018-12-11T11:59:32Z date_published: 2012-01-30T00:00:00Z date_updated: 2021-01-12T06:59:36Z day: '30' doi: 10.1090/S0273-0979-2012-01372-1 extern: 1 intvolume: ' 49' issue: '3' month: '01' page: 377 - 414 publication: Bulletin of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '4115' quality_controlled: 0 status: public title: Universality of local spectral statistics of random matrices type: journal_article volume: 49 year: '2012' ... --- _id: '2777' abstract: - lang: eng text: We consider a large neutral molecule with total nuclear charge Z in a model with self-generated classical magnetic field and where the kinetic energy of the electrons is treated relativistically. To ensure stability, we assume that Zα < 2/π, where α denotes the fine structure constant. We are interested in the ground state energy in the simultaneous limit Z → ∞, α → 0 such that κ = Zα is fixed. The leading term in the energy asymptotics is independent of κ, it is given by the Thomas-Fermi energy of order Z7/3 and it is unchanged by including the self-generated magnetic field. We prove the first correction term to this energy, the so-called Scott correction of the form S(αZ)Z2. The current paper extends the result of Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)] on the Scott correction for relativistic molecules to include a self-generated magnetic field. Furthermore, we show that the corresponding Scott correction function S, first identified by Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)], is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic fields. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Søren full_name: Fournais, Søren last_name: Fournais - first_name: Jan full_name: Solovej, Jan P last_name: Solovej citation: ama: Erdös L, Fournais S, Solovej J. Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.3697417 apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.3697417 chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Relativistic Scott Correction in Self-Generated Magnetic Fields.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.3697417. ieee: L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated magnetic fields,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012. ista: Erdös L, Fournais S, Solovej J. 2012. Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics. 53(9). mla: Erdös, László, et al. “Relativistic Scott Correction in Self-Generated Magnetic Fields.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute of Physics, 2012, doi:10.1063/1.3697417. short: L. Erdös, S. Fournais, J. Solovej, Journal of Mathematical Physics 53 (2012). date_created: 2018-12-11T11:59:32Z date_published: 2012-09-28T00:00:00Z date_updated: 2021-01-12T06:59:37Z day: '28' doi: 10.1063/1.3697417 extern: 1 intvolume: ' 53' issue: '9' month: '09' publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '4113' quality_controlled: 0 status: public title: Relativistic Scott correction in self-generated magnetic fields type: journal_article volume: 53 year: '2012' ... --- _id: '2772' abstract: - lang: eng text: We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field B. We also add the field energy β ∫ B 2 and we minimize over all magnetic fields. The parameter β effectively determines the strength of the field. We consider the weak field regime with βh 2 ≥ const > 0, where h is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order with an error bound that is smaller by a factor h 1+e{open}, i. e. the subleading term vanishes. However for potentials with a Coulomb singularity, the subleading term does not vanish due to the non-semiclassical effect of the singularity. Combined with a multiscale technique, this refined estimate is used in the companion paper (Erdo{double acute}s et al. in Scott correction for large molecules with a self-generated magnetic field, Preprint, 2011) to prove the second order Scott correction to the ground state energy of large atoms and molecules. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Søren full_name: Fournais, Søren last_name: Fournais - first_name: Jan full_name: Solovej, Jan P last_name: Solovej citation: ama: Erdös L, Fournais S, Solovej J. Second order semiclassics with self generated magnetic fields. Annales Henri Poincare. 2012;13(4):671-730. doi:10.1007/s00023-011-0150-z apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Second order semiclassics with self generated magnetic fields. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-011-0150-z chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Second Order Semiclassics with Self Generated Magnetic Fields.” Annales Henri Poincare. Birkhäuser, 2012. https://doi.org/10.1007/s00023-011-0150-z. ieee: L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self generated magnetic fields,” Annales Henri Poincare, vol. 13, no. 4. Birkhäuser, pp. 671–730, 2012. ista: Erdös L, Fournais S, Solovej J. 2012. Second order semiclassics with self generated magnetic fields. Annales Henri Poincare. 13(4), 671–730. mla: Erdös, László, et al. “Second Order Semiclassics with Self Generated Magnetic Fields.” Annales Henri Poincare, vol. 13, no. 4, Birkhäuser, 2012, pp. 671–730, doi:10.1007/s00023-011-0150-z. short: L. Erdös, S. Fournais, J. Solovej, Annales Henri Poincare 13 (2012) 671–730. date_created: 2018-12-11T11:59:31Z date_published: 2012-05-01T00:00:00Z date_updated: 2021-01-12T06:59:36Z day: '01' doi: 10.1007/s00023-011-0150-z extern: 1 intvolume: ' 13' issue: '4' month: '05' page: 671 - 730 publication: Annales Henri Poincare publication_status: published publisher: Birkhäuser publist_id: '4118' quality_controlled: 0 status: public title: Second order semiclassics with self generated magnetic fields type: journal_article volume: 13 year: '2012' ... --- _id: '2776' abstract: - lang: eng text: We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we prove (1) that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum has the same distribution as that of the Gaussian orthogonal ensemble; and (2) that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application of our method, we prove the bulk universality of generalized Wigner matrices under the assumption that the matrix entries have at least 4 + ε moments. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Antti full_name: Knowles, Antti last_name: Knowles - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau - first_name: Jun full_name: Yin, Jun last_name: Yin citation: ama: 'Erdös L, Knowles A, Yau H, Yin J. Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics. 2012;314(3):587-640. doi:10.1007/s00220-012-1527-7' apa: 'Erdös, L., Knowles, A., Yau, H., & Yin, J. (2012). Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1527-7' chicago: 'Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1527-7.' ieee: 'L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues,” Communications in Mathematical Physics, vol. 314, no. 3. Springer, pp. 587–640, 2012.' ista: 'Erdös L, Knowles A, Yau H, Yin J. 2012. Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics. 314(3), 587–640.' mla: 'Erdös, László, et al. “Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues.” Communications in Mathematical Physics, vol. 314, no. 3, Springer, 2012, pp. 587–640, doi:10.1007/s00220-012-1527-7.' short: L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics 314 (2012) 587–640. date_created: 2018-12-11T11:59:32Z date_published: 2012-09-01T00:00:00Z date_updated: 2021-01-12T06:59:37Z day: '01' doi: 10.1007/s00220-012-1527-7 extern: 1 intvolume: ' 314' issue: '3' month: '09' page: 587 - 640 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4114' quality_controlled: 0 status: public title: 'Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues' type: journal_article volume: 314 year: '2012' ... --- _id: '2774' abstract: - lang: eng text: We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given by a two term expansion c 1Z 7/3 + c 2(κ) Z 2 + o(Z 2). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Søren full_name: Fournais, Søren last_name: Fournais - first_name: Jan full_name: Solovej, Jan P last_name: Solovej citation: ama: Erdös L, Fournais S, Solovej J. Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. 2012;312(3):847-882. doi:10.1007/s00220-012-1468-1 apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1468-1 chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1468-1. ieee: L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and molecules in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 312, no. 3. Springer, pp. 847–882, 2012. ista: Erdös L, Fournais S, Solovej J. 2012. Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. 312(3), 847–882. mla: Erdös, László, et al. “Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in Mathematical Physics, vol. 312, no. 3, Springer, 2012, pp. 847–82, doi:10.1007/s00220-012-1468-1. short: L. Erdös, S. Fournais, J. Solovej, Communications in Mathematical Physics 312 (2012) 847–882. date_created: 2018-12-11T11:59:31Z date_published: 2012-06-01T00:00:00Z date_updated: 2021-01-12T06:59:36Z day: '01' doi: 10.1007/s00220-012-1468-1 extern: 1 intvolume: ' 312' issue: '3' month: '06' page: 847 - 882 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4116' quality_controlled: 0 status: public title: Scott correction for large atoms and molecules in a self-generated magnetic field type: journal_article volume: 312 year: '2012' ... --- _id: '2773' abstract: - lang: eng text: Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our work [2]. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau citation: ama: Erdös L, Yau H. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 2012;17. doi:10.1214/EJP.v17-1779 apa: Erdös, L., & Yau, H. (2012). A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v17-1779 chicago: Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2012. https://doi.org/10.1214/EJP.v17-1779. ieee: L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices,” Electronic Journal of Probability, vol. 17. Institute of Mathematical Statistics, 2012. ista: Erdös L, Yau H. 2012. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 17. mla: Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability, vol. 17, Institute of Mathematical Statistics, 2012, doi:10.1214/EJP.v17-1779. short: L. Erdös, H. Yau, Electronic Journal of Probability 17 (2012). date_created: 2018-12-11T11:59:31Z date_published: 2012-04-10T00:00:00Z date_updated: 2021-01-12T06:59:36Z day: '10' doi: 10.1214/EJP.v17-1779 extern: 1 intvolume: ' 17' month: '04' publication: Electronic Journal of Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '4117' quality_controlled: 0 status: public title: A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices type: journal_article volume: 17 year: '2012' ... --- _id: '2771' abstract: - lang: eng text: We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdos and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: David full_name: Hasler, David G last_name: Hasler citation: ama: Erdös L, Hasler D. Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. 2012;146(5):900-923. doi:10.1007/s10955-012-0445-6 apa: Erdös, L., & Hasler, D. (2012). Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-012-0445-6 chicago: Erdös, László, and David Hasler. “Anderson Localization at Band Edges for Random Magnetic Fields.” Journal of Statistical Physics. Springer, 2012. https://doi.org/10.1007/s10955-012-0445-6. ieee: L. Erdös and D. Hasler, “Anderson localization at band edges for random magnetic fields,” Journal of Statistical Physics, vol. 146, no. 5. Springer, pp. 900–923, 2012. ista: Erdös L, Hasler D. 2012. Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. 146(5), 900–923. mla: Erdös, László, and David Hasler. “Anderson Localization at Band Edges for Random Magnetic Fields.” Journal of Statistical Physics, vol. 146, no. 5, Springer, 2012, pp. 900–23, doi:10.1007/s10955-012-0445-6. short: L. Erdös, D. Hasler, Journal of Statistical Physics 146 (2012) 900–923. date_created: 2018-12-11T11:59:31Z date_published: 2012-03-01T00:00:00Z date_updated: 2021-01-12T06:59:35Z day: '01' doi: 10.1007/s10955-012-0445-6 extern: 1 intvolume: ' 146' issue: '5' month: '03' page: 900 - 923 publication: Journal of Statistical Physics publication_status: published publisher: Springer publist_id: '4119' quality_controlled: 0 status: public title: Anderson localization at band edges for random magnetic fields type: journal_article volume: 146 year: '2012' ... --- _id: '2778' abstract: - lang: eng text: We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a "convexified measure" so that the local statistics are preserved under this convexification. author: - first_name: Paul full_name: Bourgade, Paul last_name: Bourgade - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau citation: ama: Bourgade P, Erdös L, Yau H. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.4751478 apa: Bourgade, P., Erdös, L., & Yau, H. (2012). Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4751478 chicago: Bourgade, Paul, László Erdös, and Horng Yau. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.4751478. ieee: P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles with non-convex potential,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012. ista: Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9). mla: Bourgade, Paul, et al. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute of Physics, 2012, doi:10.1063/1.4751478. short: P. Bourgade, L. Erdös, H. Yau, Journal of Mathematical Physics 53 (2012). date_created: 2018-12-11T11:59:33Z date_published: 2012-09-28T00:00:00Z date_updated: 2021-01-12T06:59:38Z day: '28' doi: 10.1063/1.4751478 extern: 1 intvolume: ' 53' issue: '9' month: '09' publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '4112' quality_controlled: 0 status: public title: Bulk universality of general β-ensembles with non-convex potential type: journal_article volume: 53 year: '2012' ... --- _id: '2779' abstract: - lang: eng text: We consider a two-dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate that does not rely on the monotonicity of the energy on the random parameters. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: David full_name: Hasler, David G last_name: Hasler citation: ama: Erdös L, Hasler D. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. 2012;13(8):1719-1731. doi:10.1007/s00023-012-0177-9 apa: Erdös, L., & Hasler, D. (2012). Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-012-0177-9 chicago: Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian on ℤ 2.” Annales Henri Poincare. Birkhäuser, 2012. https://doi.org/10.1007/s00023-012-0177-9. ieee: L. Erdös and D. Hasler, “Wegner estimate for random magnetic Laplacian on ℤ 2,” Annales Henri Poincare, vol. 13, no. 8. Birkhäuser, pp. 1719–1731, 2012. ista: Erdös L, Hasler D. 2012. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. 13(8), 1719–1731. mla: Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian on ℤ 2.” Annales Henri Poincare, vol. 13, no. 8, Birkhäuser, 2012, pp. 1719–31, doi:10.1007/s00023-012-0177-9. short: L. Erdös, D. Hasler, Annales Henri Poincare 13 (2012) 1719–1731. date_created: 2018-12-11T11:59:33Z date_published: 2012-12-01T00:00:00Z date_updated: 2021-01-12T06:59:38Z day: '01' doi: 10.1007/s00023-012-0177-9 extern: 1 intvolume: ' 13' issue: '8' month: '12' page: 1719 - 1731 publication: Annales Henri Poincare publication_status: published publisher: Birkhäuser publist_id: '4111' quality_controlled: 0 status: public title: Wegner estimate for random magnetic Laplacian on ℤ 2 type: journal_article volume: 13 year: '2012' ... --- _id: '2802' abstract: - lang: eng text: When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase-separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4-40 μm are detected and tracked. Based on these data, we resolve the oscillations in the droplet size distribution that are coupled to the convective flow. author: - first_name: Tobias full_name: Lapp, Tobias last_name: Lapp - first_name: Martin full_name: Rohloff, Martin last_name: Rohloff - first_name: Jürgen full_name: Vollmer, Jürgen T last_name: Vollmer - first_name: Björn full_name: Björn Hof id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 citation: ama: Lapp T, Rohloff M, Vollmer J, Hof B. Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. 2012;52(5):1187-1200. doi:10.1007/s00348-011-1243-7 apa: Lapp, T., Rohloff, M., Vollmer, J., & Hof, B. (2012). Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. Springer. https://doi.org/10.1007/s00348-011-1243-7 chicago: Lapp, Tobias, Martin Rohloff, Jürgen Vollmer, and Björn Hof. “Particle Tracking for Polydisperse Sedimenting Droplets in Phase Separation.” Experiments in Fluids. Springer, 2012. https://doi.org/10.1007/s00348-011-1243-7. ieee: T. Lapp, M. Rohloff, J. Vollmer, and B. Hof, “Particle tracking for polydisperse sedimenting droplets in phase separation,” Experiments in Fluids, vol. 52, no. 5. Springer, pp. 1187–1200, 2012. ista: Lapp T, Rohloff M, Vollmer J, Hof B. 2012. Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. 52(5), 1187–1200. mla: Lapp, Tobias, et al. “Particle Tracking for Polydisperse Sedimenting Droplets in Phase Separation.” Experiments in Fluids, vol. 52, no. 5, Springer, 2012, pp. 1187–200, doi:10.1007/s00348-011-1243-7. short: T. Lapp, M. Rohloff, J. Vollmer, B. Hof, Experiments in Fluids 52 (2012) 1187–1200. date_created: 2018-12-11T11:59:40Z date_published: 2012-05-05T00:00:00Z date_updated: 2021-01-12T06:59:49Z day: '05' doi: 10.1007/s00348-011-1243-7 extern: 1 intvolume: ' 52' issue: '5' month: '05' page: 1187 - 1200 publication: Experiments in Fluids publication_status: published publisher: Springer publist_id: '4087' quality_controlled: 0 status: public title: Particle tracking for polydisperse sedimenting droplets in phase separation type: journal_article volume: 52 year: '2012' ... --- _id: '2803' abstract: - lang: eng text: Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border. author: - first_name: Alberto full_name: de Lózar, Alberto last_name: De Lózar - first_name: Fernando full_name: Mellibovsky, Fernando last_name: Mellibovsky - first_name: Marc full_name: Avila, Marc last_name: Avila - first_name: Björn full_name: Björn Hof id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 citation: ama: De Lózar A, Mellibovsky F, Avila M, Hof B. Edge state in pipe flow experiments. Physical Review Letters. 2012;108(21). doi:10.1103/PhysRevLett.108.214502 apa: De Lózar, A., Mellibovsky, F., Avila, M., & Hof, B. (2012). Edge state in pipe flow experiments. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.108.214502 chicago: De Lózar, Alberto, Fernando Mellibovsky, Marc Avila, and Björn Hof. “Edge State in Pipe Flow Experiments.” Physical Review Letters. American Physical Society, 2012. https://doi.org/10.1103/PhysRevLett.108.214502. ieee: A. De Lózar, F. Mellibovsky, M. Avila, and B. Hof, “Edge state in pipe flow experiments,” Physical Review Letters, vol. 108, no. 21. American Physical Society, 2012. ista: De Lózar A, Mellibovsky F, Avila M, Hof B. 2012. Edge state in pipe flow experiments. Physical Review Letters. 108(21). mla: De Lózar, Alberto, et al. “Edge State in Pipe Flow Experiments.” Physical Review Letters, vol. 108, no. 21, American Physical Society, 2012, doi:10.1103/PhysRevLett.108.214502. short: A. De Lózar, F. Mellibovsky, M. Avila, B. Hof, Physical Review Letters 108 (2012). date_created: 2018-12-11T11:59:41Z date_published: 2012-05-21T00:00:00Z date_updated: 2021-01-12T06:59:49Z day: '21' doi: 10.1103/PhysRevLett.108.214502 extern: 1 intvolume: ' 108' issue: '21' month: '05' publication: Physical Review Letters publication_status: published publisher: American Physical Society publist_id: '4086' quality_controlled: 0 status: public title: Edge state in pipe flow experiments type: journal_article volume: 108 year: '2012' ... --- _id: '2804' abstract: - lang: eng text: The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth mechanisms of the droplets. This finding establishes a gateway connecting nucleation and growth of the smallest droplets on surfaces to gross features of the evolution of the droplet size distribution author: - first_name: Johannes full_name: Blaschke, Johannes last_name: Blaschke - first_name: Tobias full_name: Lapp, Tobias last_name: Lapp - first_name: Björn full_name: Björn Hof id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 - first_name: Jürgen full_name: Vollmer, Jürgen T last_name: Vollmer citation: ama: 'Blaschke J, Lapp T, Hof B, Vollmer J. Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets. Physical Review Letters. 2012;109(6). doi:10.1103/PhysRevLett.109.068701' apa: 'Blaschke, J., Lapp, T., Hof, B., & Vollmer, J. (2012). Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.109.068701' chicago: 'Blaschke, Johannes, Tobias Lapp, Björn Hof, and Jürgen Vollmer. “Breath Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets.” Physical Review Letters. American Physical Society, 2012. https://doi.org/10.1103/PhysRevLett.109.068701.' ieee: 'J. Blaschke, T. Lapp, B. Hof, and J. Vollmer, “Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets,” Physical Review Letters, vol. 109, no. 6. American Physical Society, 2012.' ista: 'Blaschke J, Lapp T, Hof B, Vollmer J. 2012. Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets. Physical Review Letters. 109(6).' mla: 'Blaschke, Johannes, et al. “Breath Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets.” Physical Review Letters, vol. 109, no. 6, American Physical Society, 2012, doi:10.1103/PhysRevLett.109.068701.' short: J. Blaschke, T. Lapp, B. Hof, J. Vollmer, Physical Review Letters 109 (2012). date_created: 2018-12-11T11:59:41Z date_published: 2012-08-10T00:00:00Z date_updated: 2021-01-12T06:59:50Z day: '10' doi: 10.1103/PhysRevLett.109.068701 extern: 1 intvolume: ' 109' issue: '6' month: '08' publication: Physical Review Letters publication_status: published publisher: American Physical Society publist_id: '4085' quality_controlled: 0 status: public title: 'Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets' type: journal_article volume: 109 year: '2012' ... --- _id: '2825' abstract: - lang: eng text: 'We study the problem of maximum marginal prediction (MMP) in probabilistic graphical models, a task that occurs, for example, as the Bayes optimal decision rule under a Hamming loss. MMP is typically performed as a two-stage procedure: one estimates each variable''s marginal probability and then forms a prediction from the states of maximal probability. In this work we propose a simple yet effective technique for accelerating MMP when inference is sampling-based: instead of the above two-stage procedure we directly estimate the posterior probability of each decision variable. This allows us to identify the point of time when we are sufficiently certain about any individual decision. Whenever this is the case, we dynamically prune the variables we are confident about from the underlying factor graph. Consequently, at any time only samples of variables whose decision is still uncertain need to be created. Experiments in two prototypical scenarios, multi-label classification and image inpainting, show that adaptive sampling can drastically accelerate MMP without sacrificing prediction accuracy.' author: - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Lampert C. Dynamic pruning of factor graphs for maximum marginal prediction. In: Vol 1. Neural Information Processing Systems; 2012:82-90.' apa: 'Lampert, C. (2012). Dynamic pruning of factor graphs for maximum marginal prediction (Vol. 1, pp. 82–90). Presented at the NIPS: Neural Information Processing Systems, Lake Tahoe, NV, United States: Neural Information Processing Systems.' chicago: Lampert, Christoph. “Dynamic Pruning of Factor Graphs for Maximum Marginal Prediction,” 1:82–90. Neural Information Processing Systems, 2012. ieee: 'C. Lampert, “Dynamic pruning of factor graphs for maximum marginal prediction,” presented at the NIPS: Neural Information Processing Systems, Lake Tahoe, NV, United States, 2012, vol. 1, pp. 82–90.' ista: 'Lampert C. 2012. Dynamic pruning of factor graphs for maximum marginal prediction. NIPS: Neural Information Processing Systems vol. 1, 82–90.' mla: Lampert, Christoph. Dynamic Pruning of Factor Graphs for Maximum Marginal Prediction. Vol. 1, Neural Information Processing Systems, 2012, pp. 82–90. short: C. Lampert, in:, Neural Information Processing Systems, 2012, pp. 82–90. conference: end_date: 2012-12-06 location: Lake Tahoe, NV, United States name: 'NIPS: Neural Information Processing Systems' start_date: 2012-12-03 date_created: 2018-12-11T11:59:48Z date_published: 2012-12-01T00:00:00Z date_updated: 2021-01-12T06:59:59Z day: '01' department: - _id: ChLa intvolume: ' 1' language: - iso: eng month: '12' oa_version: None page: 82 - 90 publication_status: published publisher: Neural Information Processing Systems publist_id: '3975' quality_controlled: '1' scopus_import: 1 status: public title: Dynamic pruning of factor graphs for maximum marginal prediction type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 1 year: '2012' ...