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:

•	A single file of the lecture notes
•	Introduction
•	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)