Abstract:
We consider a continuous time simple random walk (CTSRW) on a finite subset of the square lattice with wired boundary conditions. This CTSRW transitions at edge rate 1 on the graph obtained from the (lattice) closure of this subset by contracting its boundary into one vertex. We study the cover time of such a walk, namely the time it takes for the walk to visit all vertices in the graph. Taking a sequence of subsets obtained as scaled lattice versions of a nice planar domain, we show that the square root of the cover time, when normalized by the size of the corresponding subset, is tight around an explicit function f(N), where N denotes the scale parameter. Our proof is based on a delicate comparison of the local time field of the walk with the extremal landscape of the discrete Gaussian Free Field on the same subset. Joint work with Marek Biskup and Oren Louidor.
Biography:
Santiago Saglietti is currently Assistant Professor at Pontificia Universidad Católica de Chile. He was a Visiting Assistant Professor at NYU Shanghai in 2020 and 2019. He obtained his PhD in 2014 from the Universidad de Buenos Aires in Argentina. He has worked in Buenos Aires as a Lecturer for Universidad de Buenos Aires and Universidad Torcuato Di Tella, and has also held postdoctoral research positions at the Pontificia Universidad Católica de Chile and the Technion Israel Institute of Science.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
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