Dimers and orthogonal polynomials: connections with random matrices

2010/04/19 by Patrik L. Ferrari, Ferrari, Patrik L.
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1004.3212

Extended lecture notes of the minicourse at IHP (5-7 October 2009); Improved version

openalex publication_date 2010/04/19 · arxiv created 2013/07/02 · arxiv updated 2013/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing structure, and the correlation functions are given in terms of a kernel. In the basic examples, the kernel is expressed in terms of orthogonal polynomials.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Related

• Random matrices and determinantal processes
• Lecture Notes on "Random Matrices"
• Lectures on random matrix theory and symmetric spaces
• Random matrices
• Random and Integrable Models in Mathematics and Physics