17 citations · 41 across the 13 of their papers we have counts for
16 papers
Phase transition for the asymptotic entropy of branching random walks on groups
Jeremie Brieussel, Robin Kaiser, Martin Klötzer +1
We consider supercritical branching random walks (BRW) on countable groups and we prove that the asymptotic entropy of the empirical distributions of the BRW has a phase transi…
Concentration inequalities for maximal displacement of random walks on groups of polynomial growth
Jérémie Brieussel, Romain Tessera, Tianyi Zheng
We prove Gaussian concentration inequalities for maximal displacement of compactly supported random walks on a compactly generated locally compact group with polynomial growth. Con…
Noise sensitivity on virtually abelian groups
Jeremie Brieussel, Ryokichi Tanaka
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 homomorp…
Furstenberg entropy spectra of stationary actions of semisimple Lie groups
Jérémie Brieussel, Tianyi Zheng
We determine Furstenberg entropy spectra of ergodic stationary actions of and its lattices. The constraints on entropy spectra are derived from a refinement of t…
Noise sensitivity of random walks on groups
Itaï Benjamini, Jérémie Brieussel
A random walk on a group is noise sensitive if resampling every step independantly with a small probability results in an almost independant output. We precisely define two notions…
Numerical upper bounds on growth of automata groups
Jérémie Brieussel, Thibault Godin, Bijan Mohammadi
The growth of a finitely generated group is an important geometric invariant which has been studied for decades. It can be either polynomial, for a well-understood class of groups,…
An automata group of intermediate growth and exponential activity
Jérémie Brieussel
We give a new example of an automata group of intermediate growth. It is generated by an automaton with 4 states on an alphabet with 8 letters. This automata group has exponential…
Shalom's property and extensions by of locally finite groups
Jérémie Brieussel, Tianyi Zheng
We show that every finitely generated extension by of a locally normally finite group has Shalom's property . This is no longer true without the norma…
Random walks on the discrete affine group
Jérémie Brieussel, Ryokichi Tanaka, Tianyi Zheng
We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of…
Connectedness of spheres in Cayley graphs
Jérémie Brieussel, Antoine Gournay
We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded f…
Speed of random walks, isoperimetry and compression of finitely generated groups
Jérémie Brieussel, Tianyi Zheng
We give a solution to the inverse problem (given a function, find a corresponding group) for large classes of speed, entropy, isoperimetric profile, return probability and -co…
About the speed of random walks on solvable groups
Jérémie Brieussel
We show that for each , there exists a solvable group and a finitely supported measure such that the associated random walk has upper speed exponent .
Discrete random walks on the group Sol
Jérémie Brieussel, Ryokichi Tanaka
The harmonic measure on the boundary of the group associated to a discrete random walk of law was described by Kaimanovich. We investigate when it is absolutely conti…
Folner sets of alternate directed groups
Jeremie Brieussel
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 valenc…
Behaviors of entropy on finitely generated groups
Jérémie Brieussel
A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any , there is a group with…
Growth behaviors in the range
Jérémie Brieussel
For every in a left neighborhood of 1, a group is constructed, the growth function of which satisfies $\limsup \frac{\log \log b_{G(α,β)}(r)}{\log r}=α…