Patrik L. Ferrari
Published 2010-04-19, updated 2013-07-02Version 2
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.
Comments: Extended lecture notes of the minicourse at IHP (5-7 October 2009); Improved version
Random matrices, non-backtracking walks, and orthogonal polynomials
Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
Four families of orthogonal polynomials of C2 and symmetric and antisymmetric generalizations of sine and cosine functions
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