Three results in directed last passage percolation
Mathematical Physics Seminar
30th October 2020, 2:00 pm – 3:00 pm
Online seminar, Zoom, meeting ID TBA
We present a few recent results for the asymptotic distribution of the last-passage time in directed last passage percolation: one in cylindrical geometry/finite temperature generalizing the Baik--Deift--Johansson theorem; one in half-quadrant stationary geometry generalizing results of Baik--Rains; and one in (possibly infinite) full-quadrant geometry with inhomogeneous weights generalizing and extending a result of Johansson and relating to the hard edge of (Jacobi and Muttalib--Borodin) random matrix ensembles. Some of these results involve distributions interpolating between the Gumbel distribution (maximum of iid random variables) and the Tracy--Widom distribution (maximum of correlated point processes). This is based on joint work (and work in progress) with Jeremie Bouttier, Patrik Ferrari, and Alessandra Occelli.