Summer School: Beg Rohu 2008

Random matrices and related problems

Content: In this lecture we will explore some aspects of random matrix theory. We will then apply the same underlying mathematical structure to a couple of models of statistical mechanics.

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Scanned lectures notes:

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Gaussian Unitary / Orthogonal Ensembles of random matrices (GUE / GOE)
Determinantal point processes
Edge scaling limit and Tracy-Widom distributions
Extended determinantal point processes
Application to the polynuclear growth model in the droplet geometry (PNG droplet)
Application to the Totally Asymmetric Simple Exclusion Process (TASEP)