Lower and moderate deviation for maximums of branching random walk and branching Brownian motion

Jeudi 7 novembre 2019 15:45-16:45 - Xinxin Chen - ICJ, Université Claude Bernard, Lyon

Résumé : For a supercritical branching random walk on real line, it is proved by Bramson (1983) and Aïdékon (2013) that M_n, the maximal position at time n, shifted by its median m_n=x^* n-\frac32\theta^* \log n+\Theta(1), converges in law under some mild condition. We study the lower and moderate deviation for this convergence. Moreover, for branching Brownian motion, we study the process conditioned on small maximum. This is based on joint works with Hui He and Bastien Mallein.

Lower and moderate deviation for maximums of branching random walk and branching Brownian motion  Version PDF