# Student Probability Seminar

#### Last Passage Percolation and Random Matrices

Speaker: Lucas Begnini

Location: Warren Weaver Hall 1314

Date: Thursday, February 18, 2016, 4 p.m.

Synopsis:

We'll start with the description of last passage percolation (LPP) and some other interpretations of that model. We'll then look at the results given by Johansson that creates a link between LPP and random matrix theory : the similarity between the distribution of the LPP model and the largest eigenvalue of some random matrix ensembles. We'll see that by using random matrix theory tools such as orthogonal polynomials and its asymptotics, we can obtain the same type of central limit theorem with fluctuations given by the Tracy-Widom distribution. We'll then look at the combinatorial proof, using the Robinson-Schensted-Knuth correspondence and Schur polynomials, that gives the distribution of the LPP. Finally, If we have enough time, we'll look at some more recent results/improvements in last passage percolation theory.