arXiv subjects

Jeremie Brieussel

Publications and source records attributed to Jeremie Brieussel.

3 recordsLinked to original sources

arXiv2026

Phase transition for the asymptotic entropy of branching random walks on groups

We consider supercritical branching random walks (BRW) on countable groups $G$ and we prove that the asymptotic entropy of the empirical distributions of the BRW has a phase transition at $\rho_* = e^{h(\mu)}$, where $h(\mu)$ is the asymptotic entropy of the underlying random walk on $G$ with step distribution $\mu$. Below this value $\rho_*$, the asymptotic empirical entropy of BRW equals the logarithm of the exponential growth rate of the population. Above this value, it is constantly equal to the asymptotic entropy of the underlying random walk. In particular, this answers questions from Kaimanovich-Woess [MR4663513, Section 6.3] about the existence and the behavior of the asymptotic entropy.

math.PR↗

arXiv2025

Noise sensitivity on virtually abelian groups

We show that aperiodic random walks with finite second moment on virtually abelian groups are noise sensitive in total variation if and only if the group admits no nonzero homomorphism onto the infinite cyclic group.

math.PR↗

arXiv2013

Folner sets of alternate directed groups

An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.

math.GR↗