A Scaling Limit for the Cover Time of the Binary Tree

A Scaling Limit for the Cover Time of the Binary Tree
Date & Time: 
Tuesday, April 2, 2019 - 11:00 to 12:00
Santiago Saglietti, NYU Shanghai
Room 264, Geography Building, Zhongbei Campus, East China Normal University


We consider a continuous time random walk on the rooted binary tree of depth n with all transition rates equal to one and study its cover time, namely the time until all vertices of the tree have been visited. We prove that, normalized by 2^{n+1}n and then centered by (log2)n-log n, the cover time admits a weak limit as the depth of the tree tends to infinity. The limiting distribution is identified as that of a randomly shifted Gumbel random variable with rate one, where the shift is given by the sum of the limits of the derivative martingales associated with two negatively correlated discrete Gaussian free fields on the infinite version of the tree. The existence of the limit and its overall form were conjectured in the literature. Our approach is quite different from those taken in earlier works on this subject and relies in great part on a comparison with the extremal landscape of the discrete Gaussian free field. Joint work with Aser Cortines and Oren Louidor.


Santiago Saglietti is a Visiting Assistant Professor at NYU Shanghai. 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.  His research interests lie in mathematical statistical mechanics, stochastic processes (theory and applications), branching processes, random walks and random walks in random environments.


Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai