András Mészáros

I am a Postdoctoral Fellow at the Alfréd Rényi Institute of Mathematics.
For three years, I was a Brauer Postdoctoral Fellow at University of Toronto Scarborough, Department of Computer and Mathematical Sciences mentored by Bálint Virág. I returned to Hungary in 2024.
I obtained my PhD at Central European University in 2021. My advisor was Miklós Abért. My Math Genealogy page.

My research is supported by the Marie Sklodowska-Curie Postdoctoral Fellowship "Random complexes and the Cohen-Lenstra heuristics" and the NKKP Starting grant "Homology of random simplicial complexes, Cohen-Lenstra heuristics and graph limits".

Research interest: Random matrices, graphs and simplicial complexes; Graph limits; Algebraic and spectral graph theory; Random processes on graphs

CV

E-mail: meszaros (at) renyi.hu

Google Scholar

Publications:

• The rank evolution of block bidiagonal matrices over finite fields, 2025 preprint
• Universal constant order fluctuations for the cokernels of block lower triangular matrices, 2024 preprint
• A phase transition for the cokernels of random band matrices over the p-adic integers, 2024 preprint
• The 2-torsion of determinantal hypertrees is not Cohen-Lenstra, 2024, To appear in Israel Journal of Mathematics, preprint
• Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees, Combinatorica 45, 17 (2025) published version, preprint
• Coboundary expansion for the union of determinantal hypertrees, Random Structures & Algorithms 65 (4), 896-914, 2024, published version, preprint
• (with Yuri Bakhtin, Konstantin Khanin and Jeremy Voltz) Last passage percolation in a product-type random environment, 2023, To appear in Annales de l’Institut Henri Poincare (B) Probability and Statistics, preprint
• Cohen-Lenstra distribution for sparse matrices with determinantal biasing, International Mathematics Research Notices, 2025(3), 1–19, published version, preprint
• (with Bálint Virág) Eigenvectors of the square grid plus GUE, Communications in Mathematical Physics 405 (1), 1-49, 2024, published version, preprint, a talk
• The local weak limit of k-dimensional hypertrees. Transactions of the American Mathematical Society, 375 (2022), 6127-6154, published version, preprint
• On the free energy density of factor models on biregular graphs, 2020 preprint
• Matchings on trees and the adjacency matrix: A determinantal viewpoint, Random Structures & Algorithms 63(3), 753-778, 2023. published version, preprint
• A BK inequality for random matchings, Combinatorics, Probability and Computing 32 (1), 151-157, 2023. published version, preprint
• (with Ferenc Bencs) Atoms of the matching measure, Electron. J. Probab. 27 1 - 38, 2022. published version, preprint
• Limiting entropy of determinantal processes. Annals of Probability, Volume 48, Number 5 (2020), 2615-2643. published version, preprint
• The distribution of sandpile groups of random regular graphs. Transactions of the American Mathematical Society, 373 (2020), 6529-6594 published version, preprint
• A note on disjoint dijoins. Combinatorica 38, 1485–1488 (2018). published version, preprint
• New bounds for 3-part Sperner families. Moscow J. Combin.Number Theory, 5:255-273, (2015) published version

Selected past talks:

• CMS Winter Meeting, December 1-4, 2023. Montreal, Canada
• Measured Group Theory, Stochastic Processes on Groups and Borel Combinatorics, April 22-May 26, 2023. Luminy, France
• (Poster at) The 24th Midrasha Mathematicae: Random Schrödinger Operators and Random Matrices, May 14-18, 2023. Jerusalem, Israel
• Random Matrix Eurasia, April 18-May 13, 2022. Singapore
• TDA week, Feb 14-18, 2022. Japan (online)
• Algebraic questions in random integral matrices, November 14-15, 2020. Columbus, Ohio
• UW-Madison Probability Seminar, August 10, 2018. Madison, Wisconsin
• Zamecek workshop on Analytic combinatorics, 2017
• Summit 240, July 7-11, 2014. Budapest

Last update: April 17, 2025