Why random matrices share universal processes with interacting particle systems?

2013/12/04 by Patrik L. Ferrari, Ferrari, Patrik L. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1312.1126

Extended lecture notes of the ICTP minicourse in Trieste, September 2013. 45 pages, 6 figures; Minor corrections

openalex publication_date 2013/12/04 · arxiv created 2013/12/16 · arxiv updated 2013/12/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy₂ process, arise both in random matrices and interacting particle systems. The link is through a common mathematical structure on an interlacing structure, also known as Gelfand-Tsetlin pattern, that appears for specific models in both fields.

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