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Dan Betea: From Gumbel to Tracy–Widom in last passage percolation

Tid: Ti 2021-11-09 kl 15.20

Plats: Zoom, meeting ID: 698 3346 0369

Föreläsare: Dan Betea (KU Leuven)

Abstract

We survey a couple of discrete probabilistic (and integrable) models with extreme statistics interpolating, asymptotically, between the Gumbel and the Tracy–Widom distributions. These laws appear in opposite probabilistic corners: maxima of iid random variables (Gumbel) and maxima of correlated systems like eigenvalues of hermitian matrices (Tracy–Widom). Both models we describe are discrete models of last passage percolation (on a cylinder and in an inhomogeneous infinite quadrant respectively), and shadow in some sense previous continuous models studied by Johansson (the Moshe–Neuberger–Shapiro random matrix model and a similar continuous LPP model). In both cases the asymptotics of LPP times resemble those at the edge of random matrices: in one case we obtain the finite temperature Tracy–Widom distribution of Johansson, and in another case the hard-edge random matrix Bessel kernel in exponential coordinates (again of Johansson). The results are based on joint work with Jérémie Bouttier (Math. Phys. Anal. Geom. 2019, arXiv:1807.09022) and Alessandra Occelli (arXiv:2012.01995 and arXiv:2011.07890).