Dimers and orthogonal polynomials: connections with random matrices

Details Dimers and orthogonal polynomials: connections with random matrices Dimers and orthogonal polynomials: connections with random matrices

2010-04-19

arxiv.org/abs/1004.3212v1

Physics

Mathematical Physics

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

Scientific paper

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.

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