Session S04 - Random Walks and Related Topics

Thursday, July 15, 15:00 ~ 15:30 UTC-3

Non-intersecting Brownian motions and random matrices

Daniel Remenik

Universidad de Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A well known result shows that the rescaled maximal height of a system of N non-intersecting Brownian bridges starting and ending at the origin converges, as N goes to infinity, to the Tracy-Widom GOE random variable from random matrix theory. In this talk I will discuss some recent extensions of this result, involving the distribution of the height of a fixed number of paths and of the maximal height on an interval, as well as the asymptotic distribution in the case when a few paths at the top start and end at arbitrary locations. I will describe results which connect these distributions to other random matrix ensembles as well as to KPZ fluctuations and certain PDEs.

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