--- _id: '9567' abstract: - lang: eng text: Let P be a graph property which is preserved by removal of edges, and consider the random graph process that starts with the empty n-vertex graph and then adds edges one-by-one, each chosen uniformly at random subject to the constraint that P is not violated. These types of random processes have been the subject of extensive research over the last 20 years, having striking applications in extremal combinatorics, and leading to the discovery of important probabilistic tools. In this paper we consider the k-matching-free process, where P is the property of not containing a matching of size k. We are able to analyse the behaviour of this process for a wide range of values of k; in particular we prove that if k=o(n) or if n−2k=o(n−−√/logn) then this process is likely to terminate in a k-matching-free graph with the maximum possible number of edges, as characterised by Erdős and Gallai. We also show that these bounds on k are essentially best possible, and we make a first step towards understanding the behaviour of the process in the intermediate regime. article_processing_charge: No article_type: original author: - first_name: Michael full_name: Krivelevich, Michael last_name: Krivelevich - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 - first_name: Po‐Shen full_name: Loh, Po‐Shen last_name: Loh - first_name: Benny full_name: Sudakov, Benny last_name: Sudakov citation: ama: Krivelevich M, Kwan MA, Loh P, Sudakov B. The random k‐matching‐free process. Random Structures and Algorithms. 2018;53(4):692-716. doi:10.1002/rsa.20814 apa: Krivelevich, M., Kwan, M. A., Loh, P., & Sudakov, B. (2018). The random k‐matching‐free process. Random Structures and Algorithms. Wiley. https://doi.org/10.1002/rsa.20814 chicago: Krivelevich, Michael, Matthew Alan Kwan, Po‐Shen Loh, and Benny Sudakov. “The Random K‐matching‐free Process.” Random Structures and Algorithms. Wiley, 2018. https://doi.org/10.1002/rsa.20814. ieee: M. Krivelevich, M. A. Kwan, P. Loh, and B. Sudakov, “The random k‐matching‐free process,” Random Structures and Algorithms, vol. 53, no. 4. Wiley, pp. 692–716, 2018. ista: Krivelevich M, Kwan MA, Loh P, Sudakov B. 2018. The random k‐matching‐free process. Random Structures and Algorithms. 53(4), 692–716. mla: Krivelevich, Michael, et al. “The Random K‐matching‐free Process.” Random Structures and Algorithms, vol. 53, no. 4, Wiley, 2018, pp. 692–716, doi:10.1002/rsa.20814. short: M. Krivelevich, M.A. Kwan, P. Loh, B. Sudakov, Random Structures and Algorithms 53 (2018) 692–716. date_created: 2021-06-18T12:37:40Z date_published: 2018-12-01T00:00:00Z date_updated: 2023-02-23T14:01:07Z day: '01' doi: 10.1002/rsa.20814 extern: '1' external_id: arxiv: - '1708.01054' intvolume: ' 53' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.01054 month: '12' oa: 1 oa_version: Preprint page: 692-716 publication: Random Structures and Algorithms publication_identifier: eissn: - 1098-2418 issn: - 1042-9832 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: The random k‐matching‐free process type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 53 year: '2018' ... --- _id: '9565' abstract: - lang: eng text: Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if p≥(logn+ω(1))/n then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically n!(p(1+o(1)))n. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically n!(logn/n(1+o(1)))n directed Hamilton cycles. article_processing_charge: No article_type: original author: - first_name: Asaf full_name: Ferber, Asaf last_name: Ferber - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 - first_name: Benny full_name: Sudakov, Benny last_name: Sudakov citation: ama: Ferber A, Kwan MA, Sudakov B. Counting Hamilton cycles in sparse random directed graphs. Random Structures and Algorithms. 2018;53(4):592-603. doi:10.1002/rsa.20815 apa: Ferber, A., Kwan, M. A., & Sudakov, B. (2018). Counting Hamilton cycles in sparse random directed graphs. Random Structures and Algorithms. Wiley. https://doi.org/10.1002/rsa.20815 chicago: Ferber, Asaf, Matthew Alan Kwan, and Benny Sudakov. “Counting Hamilton Cycles in Sparse Random Directed Graphs.” Random Structures and Algorithms. Wiley, 2018. https://doi.org/10.1002/rsa.20815. ieee: A. Ferber, M. A. Kwan, and B. Sudakov, “Counting Hamilton cycles in sparse random directed graphs,” Random Structures and Algorithms, vol. 53, no. 4. Wiley, pp. 592–603, 2018. ista: Ferber A, Kwan MA, Sudakov B. 2018. Counting Hamilton cycles in sparse random directed graphs. Random Structures and Algorithms. 53(4), 592–603. mla: Ferber, Asaf, et al. “Counting Hamilton Cycles in Sparse Random Directed Graphs.” Random Structures and Algorithms, vol. 53, no. 4, Wiley, 2018, pp. 592–603, doi:10.1002/rsa.20815. short: A. Ferber, M.A. Kwan, B. Sudakov, Random Structures and Algorithms 53 (2018) 592–603. date_created: 2021-06-18T12:06:28Z date_published: 2018-12-01T00:00:00Z date_updated: 2023-02-23T14:01:03Z day: '01' doi: 10.1002/rsa.20815 extern: '1' external_id: arxiv: - '1708.07746' intvolume: ' 53' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.07746 month: '12' oa: 1 oa_version: Preprint page: 592-603 publication: Random Structures and Algorithms publication_identifier: eissn: - 1098-2418 issn: - 1042-9832 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Counting Hamilton cycles in sparse random directed graphs type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 53 year: '2018' ... --- _id: '9568' abstract: - lang: eng text: An intercalate in a Latin square is a 2×2 Latin subsquare. Let N be the number of intercalates in a uniformly random n×n Latin square. We prove that asymptotically almost surely N≥(1−o(1))n2/4, and that EN≤(1+o(1))n2/2 (therefore asymptotically almost surely N≤fn2 for any f→∞). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares. article_processing_charge: No article_type: original author: - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 - first_name: Benny full_name: Sudakov, Benny last_name: Sudakov citation: ama: Kwan MA, Sudakov B. Intercalates and discrepancy in random Latin squares. Random Structures and Algorithms. 2018;52(2):181-196. doi:10.1002/rsa.20742 apa: Kwan, M. A., & Sudakov, B. (2018). Intercalates and discrepancy in random Latin squares. Random Structures and Algorithms. Wiley. https://doi.org/10.1002/rsa.20742 chicago: Kwan, Matthew Alan, and Benny Sudakov. “Intercalates and Discrepancy in Random Latin Squares.” Random Structures and Algorithms. Wiley, 2018. https://doi.org/10.1002/rsa.20742. ieee: M. A. Kwan and B. Sudakov, “Intercalates and discrepancy in random Latin squares,” Random Structures and Algorithms, vol. 52, no. 2. Wiley, pp. 181–196, 2018. ista: Kwan MA, Sudakov B. 2018. Intercalates and discrepancy in random Latin squares. Random Structures and Algorithms. 52(2), 181–196. mla: Kwan, Matthew Alan, and Benny Sudakov. “Intercalates and Discrepancy in Random Latin Squares.” Random Structures and Algorithms, vol. 52, no. 2, Wiley, 2018, pp. 181–96, doi:10.1002/rsa.20742. short: M.A. Kwan, B. Sudakov, Random Structures and Algorithms 52 (2018) 181–196. date_created: 2021-06-18T12:47:25Z date_published: 2018-03-01T00:00:00Z date_updated: 2023-02-23T14:01:09Z day: '01' doi: 10.1002/rsa.20742 extern: '1' external_id: arxiv: - '1607.04981' intvolume: ' 52' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1607.04981 month: '03' oa: 1 oa_version: Preprint page: 181-196 publication: Random Structures and Algorithms publication_identifier: eissn: - 1098-2418 issn: - 1042-9832 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Intercalates and discrepancy in random Latin squares type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 52 year: '2018' ... --- _id: '9587' abstract: - lang: eng text: We say a family of sets is intersecting if any two of its sets intersect, and we say it is trivially intersecting if there is an element which appears in every set of the family. In this paper we study the maximum size of a non-trivially intersecting family in a natural “multi-part” setting. Here the ground set is divided into parts, and one considers families of sets whose intersection with each part is of a prescribed size. Our work is motivated by classical results in the single-part setting due to Erdős, Ko and Rado, and Hilton and Milner, and by a theorem of Frankl concerning intersecting families in this multi-part setting. In the case where the part sizes are sufficiently large we determine the maximum size of a non-trivially intersecting multi-part family, disproving a conjecture of Alon and Katona. article_processing_charge: No article_type: original author: - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 - first_name: Benny full_name: Sudakov, Benny last_name: Sudakov - first_name: Pedro full_name: Vieira, Pedro last_name: Vieira citation: ama: Kwan MA, Sudakov B, Vieira P. Non-trivially intersecting multi-part families. Journal of Combinatorial Theory Series A. 2018;156:44-60. doi:10.1016/j.jcta.2017.12.001 apa: Kwan, M. A., Sudakov, B., & Vieira, P. (2018). Non-trivially intersecting multi-part families. Journal of Combinatorial Theory Series A. Elsevier. https://doi.org/10.1016/j.jcta.2017.12.001 chicago: Kwan, Matthew Alan, Benny Sudakov, and Pedro Vieira. “Non-Trivially Intersecting Multi-Part Families.” Journal of Combinatorial Theory Series A. Elsevier, 2018. https://doi.org/10.1016/j.jcta.2017.12.001. ieee: M. A. Kwan, B. Sudakov, and P. Vieira, “Non-trivially intersecting multi-part families,” Journal of Combinatorial Theory Series A, vol. 156. Elsevier, pp. 44–60, 2018. ista: Kwan MA, Sudakov B, Vieira P. 2018. Non-trivially intersecting multi-part families. Journal of Combinatorial Theory Series A. 156, 44–60. mla: Kwan, Matthew Alan, et al. “Non-Trivially Intersecting Multi-Part Families.” Journal of Combinatorial Theory Series A, vol. 156, Elsevier, 2018, pp. 44–60, doi:10.1016/j.jcta.2017.12.001. short: M.A. Kwan, B. Sudakov, P. Vieira, Journal of Combinatorial Theory Series A 156 (2018) 44–60. date_created: 2021-06-22T11:42:48Z date_published: 2018-05-01T00:00:00Z date_updated: 2023-02-23T14:01:55Z day: '01' doi: 10.1016/j.jcta.2017.12.001 extern: '1' external_id: arxiv: - '1703.09946' intvolume: ' 156' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1703.09946 month: '05' oa: 1 oa_version: Preprint page: 44-60 publication: Journal of Combinatorial Theory Series A publication_identifier: issn: - 0097-3165 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Non-trivially intersecting multi-part families type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 156 year: '2018' ... --- _id: '9665' abstract: - lang: eng text: We investigate the thermodynamics and kinetics of a hydrogen interstitial in magnetic α-iron, taking account of the quantum fluctuations of the proton as well as the anharmonicities of lattice vibrations and hydrogen hopping. We show that the diffusivity of hydrogen in the lattice of bcc iron deviates strongly from an Arrhenius behavior at and below room temperature. We compare a quantum transition state theory to explicit ring polymer molecular dynamics in the calculation of diffusivity. We then address the trapping of hydrogen by a vacancy as a prototype lattice defect. By a sequence of steps in a thought experiment, each involving a thermodynamic integration, we are able to separate out the binding free energy of a proton to a defect into harmonic and anharmonic, and classical and quantum contributions. We find that about 30% of a typical binding free energy of hydrogen to a lattice defect in iron is accounted for by finite temperature effects, and about half of these arise from quantum proton fluctuations. This has huge implications for the comparison between thermal desorption and permeation experiments and standard electronic structure theory. The implications are even greater for the interpretation of muon spin resonance experiments. article_number: '225901' article_processing_charge: No article_type: review author: - first_name: Bingqing full_name: Cheng, Bingqing id: cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9 last_name: Cheng orcid: 0000-0002-3584-9632 - first_name: Anthony T. full_name: Paxton, Anthony T. last_name: Paxton - first_name: Michele full_name: Ceriotti, Michele last_name: Ceriotti citation: ama: 'Cheng B, Paxton AT, Ceriotti M. Hydrogen diffusion and trapping in α-iron: The role of quantum and anharmonic fluctuations. Physical Review Letters. 2018;120(22). doi:10.1103/physrevlett.120.225901' apa: 'Cheng, B., Paxton, A. T., & Ceriotti, M. (2018). Hydrogen diffusion and trapping in α-iron: The role of quantum and anharmonic fluctuations. Physical Review Letters. American Physical Society. https://doi.org/10.1103/physrevlett.120.225901' chicago: 'Cheng, Bingqing, Anthony T. Paxton, and Michele Ceriotti. “Hydrogen Diffusion and Trapping in α-Iron: The Role of Quantum and Anharmonic Fluctuations.” Physical Review Letters. American Physical Society, 2018. https://doi.org/10.1103/physrevlett.120.225901.' ieee: 'B. Cheng, A. T. Paxton, and M. Ceriotti, “Hydrogen diffusion and trapping in α-iron: The role of quantum and anharmonic fluctuations,” Physical Review Letters, vol. 120, no. 22. American Physical Society, 2018.' ista: 'Cheng B, Paxton AT, Ceriotti M. 2018. Hydrogen diffusion and trapping in α-iron: The role of quantum and anharmonic fluctuations. Physical Review Letters. 120(22), 225901.' mla: 'Cheng, Bingqing, et al. “Hydrogen Diffusion and Trapping in α-Iron: The Role of Quantum and Anharmonic Fluctuations.” Physical Review Letters, vol. 120, no. 22, 225901, American Physical Society, 2018, doi:10.1103/physrevlett.120.225901.' short: B. Cheng, A.T. Paxton, M. Ceriotti, Physical Review Letters 120 (2018). date_created: 2021-07-15T12:22:41Z date_published: 2018-06-01T00:00:00Z date_updated: 2021-08-09T12:36:22Z day: '01' doi: 10.1103/physrevlett.120.225901 extern: '1' external_id: arxiv: - '1803.00600' pmid: - '29906144' intvolume: ' 120' issue: '22' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1803.00600 month: '06' oa: 1 oa_version: Preprint pmid: 1 publication: Physical Review Letters publication_identifier: eissn: - 1079-7114 issn: - 0031-9007 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: 'Hydrogen diffusion and trapping in α-iron: The role of quantum and anharmonic fluctuations' type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 120 year: '2018' ...