Dimers and orthogonal polynomials: connections with random matrices
Mathematical Physics
2013-07-03 v2 math.MP
Probability
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.
Cite
@article{arxiv.1004.3212,
title = {Dimers and orthogonal polynomials: connections with random matrices},
author = {Patrik L. Ferrari},
journal= {arXiv preprint arXiv:1004.3212},
year = {2013}
}
Comments
Extended lecture notes of the minicourse at IHP (5-7 October 2009); Improved version