[{"oa":1,"quality_controlled":"1","publisher":"World Scientific Publishing","acknowledgement":"This work was supported by the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo. 694227).","date_created":"2022-03-18T08:11:34Z","date_published":"2021-02-01T00:00:00Z","doi":"10.1142/s0129055x20600120","year":"2021","isi":1,"publication":"Reviews in Mathematical Physics","day":"01","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"article_number":"2060012","article_processing_charge":"No","external_id":{"arxiv":["1912.12509"],"isi":["000613313200013"]},"author":[{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"title":"The polaron at strong coupling","citation":{"ama":"Seiringer R. The polaron at strong coupling. Reviews in Mathematical Physics. 2021;33(01). doi:10.1142/s0129055x20600120","apa":"Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120","short":"R. Seiringer, Reviews in Mathematical Physics 33 (2021).","ieee":"R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical Physics, vol. 33, no. 01. World Scientific Publishing, 2021.","mla":"Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120.","ista":"Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical Physics. 33(01), 2060012.","chicago":"Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","main_file_link":[{"url":"https://arxiv.org/abs/1912.12509","open_access":"1"}],"scopus_import":"1","intvolume":" 33","month":"02","abstract":[{"lang":"eng","text":" We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass."}],"oa_version":"Preprint","ec_funded":1,"volume":33,"issue":"01","publication_status":"published","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","_id":"10852","department":[{"_id":"RoSe"}],"date_updated":"2023-09-05T16:08:02Z"},{"file_date_updated":"2021-02-03T10:37:28Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"ddc":["006","514","516"],"date_updated":"2023-09-07T13:29:01Z","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","_id":"9056","license":"https://creativecommons.org/licenses/by/4.0/","related_material":{"record":[{"status":"public","id":"187","relation":"part_of_dissertation"},{"status":"public","id":"8703","relation":"part_of_dissertation"}]},"language":[{"iso":"eng"}],"file":[{"file_name":"thesis_source.zip","date_created":"2021-02-02T14:09:25Z","file_size":13446994,"date_updated":"2021-02-03T10:37:28Z","creator":"patrickd","file_id":"9063","checksum":"bcf27986147cab0533b6abadd74e7629","content_type":"application/zip","relation":"source_file","access_level":"closed"},{"date_created":"2021-02-02T14:09:18Z","file_name":"thesis_pdfA2b.pdf","date_updated":"2021-02-02T14:09:18Z","file_size":5210329,"creator":"patrickd","file_id":"9064","checksum":"9cc8af266579a464385bbe2aff6af606","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"month":"02","place":"Klosterneuburg","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","abstract":[{"text":"In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets.","lang":"eng"}],"title":"Multi-cover persistence and Delaunay mosaics","article_processing_charge":"No","author":[{"last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021.","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056","apa":"Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056","chicago":"Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria."},"date_created":"2021-02-02T14:11:06Z","date_published":"2021-02-01T00:00:00Z","doi":"10.15479/AT:ISTA:9056","page":"134","day":"01","year":"2021","has_accepted_license":"1","oa":1,"publisher":"Institute of Science and Technology Austria"},{"status":"public","type":"dissertation","_id":"9022","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2021-01-25T14:19:10Z","ddc":["510"],"supervisor":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"date_updated":"2023-09-07T13:29:32Z","month":"01","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices."}],"ec_funded":1,"file":[{"success":1,"file_id":"9043","checksum":"5a93658a5f19478372523ee232887e2b","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"thesis.pdf","date_created":"2021-01-25T14:19:03Z","file_size":4127796,"date_updated":"2021-01-25T14:19:03Z","creator":"gcipollo"},{"access_level":"closed","relation":"source_file","content_type":"application/zip","file_id":"9044","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","creator":"gcipollo","date_updated":"2021-01-25T14:19:10Z","file_size":12775206,"date_created":"2021-01-25T14:19:10Z","file_name":"Thesis_files.zip"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385"},{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"Fluctuations in the spectrum of random matrices","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022","apa":"Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022","mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022.","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022."},"publisher":"Institute of Science and Technology Austria","oa":1,"acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.","date_published":"2021-01-25T00:00:00Z","doi":"10.15479/AT:ISTA:9022","date_created":"2021-01-21T18:16:54Z","page":"380","day":"25","has_accepted_license":"1","year":"2021"},{"ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Phuong, Mary, and Christoph Lampert. “The Inductive Bias of ReLU Networks on Orthogonally Separable Data.” In 9th International Conference on Learning Representations, 2021.","ista":"Phuong M, Lampert C. 2021. The inductive bias of ReLU networks on orthogonally separable data. 9th International Conference on Learning Representations. ICLR: International Conference on Learning Representations.","mla":"Phuong, Mary, and Christoph Lampert. “The Inductive Bias of ReLU Networks on Orthogonally Separable Data.” 9th International Conference on Learning Representations, 2021.","short":"M. Phuong, C. Lampert, in:, 9th International Conference on Learning Representations, 2021.","ieee":"M. Phuong and C. Lampert, “The inductive bias of ReLU networks on orthogonally separable data,” in 9th International Conference on Learning Representations, Virtual, 2021.","apa":"Phuong, M., & Lampert, C. (2021). The inductive bias of ReLU networks on orthogonally separable data. In 9th International Conference on Learning Representations. Virtual.","ama":"Phuong M, Lampert C. The inductive bias of ReLU networks on orthogonally separable data. In: 9th International Conference on Learning Representations. ; 2021."},"date_updated":"2023-09-07T13:29:50Z","title":"The inductive bias of ReLU networks on orthogonally separable data","file_date_updated":"2021-05-24T11:15:57Z","department":[{"_id":"GradSch"},{"_id":"ChLa"}],"article_processing_charge":"No","author":[{"full_name":"Bui Thi Mai, Phuong","last_name":"Bui Thi Mai","id":"3EC6EE64-F248-11E8-B48F-1D18A9856A87","first_name":"Phuong"},{"id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","first_name":"Christoph","orcid":"0000-0001-8622-7887","full_name":"Lampert, Christoph","last_name":"Lampert"}],"_id":"9416","status":"public","conference":{"name":" ICLR: International Conference on Learning Representations","location":"Virtual","end_date":"2021-05-07","start_date":"2021-05-03"},"type":"conference","language":[{"iso":"eng"}],"publication":"9th International Conference on Learning Representations","day":"01","file":[{"file_id":"9417","checksum":"f34ff17017527db5ba6927f817bdd125","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"iclr2021_conference.pdf","date_created":"2021-05-24T11:15:57Z","file_size":502356,"date_updated":"2021-05-24T11:15:57Z","creator":"bphuong"}],"publication_status":"published","year":"2021","has_accepted_license":"1","date_created":"2021-05-24T11:16:46Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"9418"}]},"date_published":"2021-05-01T00:00:00Z","oa_version":"Published Version","abstract":[{"text":"We study the inductive bias of two-layer ReLU networks trained by gradient flow. We identify a class of easy-to-learn (`orthogonally separable') datasets, and characterise the solution that ReLU networks trained on such datasets converge to. Irrespective of network width, the solution turns out to be a combination of two max-margin classifiers: one corresponding to the positive data subset and one corresponding to the negative data subset. The proof is based on the recently introduced concept of extremal sectors, for which we prove a number of properties in the context of orthogonal separability. In particular, we prove stationarity of activation patterns from some time onwards, which enables a reduction of the ReLU network to an ensemble of linear subnetworks.","lang":"eng"}],"month":"05","main_file_link":[{"url":"https://openreview.net/pdf?id=krz7T0xU9Z_","open_access":"1"}],"oa":1,"scopus_import":"1","quality_controlled":"1"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in Mathematical Physics, vol. 111, 19, Springer Nature, 2021, doi:10.1007/s11005-020-01350-5.","ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the spectral gap for the Landau–Pekar equations,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical Physics 111 (2021).","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-020-01350-5","apa":"Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2021). Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01350-5","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-020-01350-5.","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19."},"title":"Persistence of the spectral gap for the Landau–Pekar equations","external_id":{"isi":["000617195700001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"last_name":"Rademacher","full_name":"Rademacher, Simone Anna Elvira","orcid":"0000-0001-5059-4466","id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"article_number":"19","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication":"Letters in Mathematical Physics","day":"11","year":"2021","has_accepted_license":"1","isi":1,"date_created":"2021-03-07T23:01:25Z","date_published":"2021-02-11T00:00:00Z","doi":"10.1007/s11005-020-01350-5","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged. Open Access funding provided by Institute of Science and Technology (IST Austria)","oa":1,"publisher":"Springer Nature","quality_controlled":"1","ddc":["510"],"date_updated":"2023-09-07T13:30:11Z","file_date_updated":"2021-03-09T11:44:34Z","department":[{"_id":"RoSe"}],"_id":"9225","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"file":[{"file_name":"2021_LettersMathPhysics_Feliciangeli.pdf","date_created":"2021-03-09T11:44:34Z","creator":"dernst","file_size":391205,"date_updated":"2021-03-09T11:44:34Z","success":1,"checksum":"ffbfe1aad623bce7ff529c207e343b53","file_id":"9232","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"issn":["03779017"],"eissn":["15730530"]},"ec_funded":1,"volume":111,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"9733"}]},"oa_version":"Published Version","abstract":[{"text":"The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere, we provide a class of initial data for which the associated effective Hamiltonian\r\nhas a uniform spectral gap for all times. For such initial data, this allows us to extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations and their derivation\r\nfrom the Fröhlich model obtained in previous works to larger times.","lang":"eng"}],"intvolume":" 111","month":"02","scopus_import":"1"}]