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04 02 IM Noticia ProbabilitySeminarTítulo: "Weak convergence for the scaled cover time of the rooted binary tree"
Palestrante: Santiago Saglietti

Data: 03/03/2021
Horário: 11h às 12h
Local: Transmissão Online

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Resumo: 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 unique solution to a specific distributional equation. The existence of the limit and its overall form were conjectured in the literature. However, our approach is 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.