Timoth'ee B'enard

activity

20202026

most citedMultislicing and effective equidistribution for random walks on some homogeneous spaces

1 citations · 2 across the 13 of their papers we have counts for

collaborators

15 papers

math.DS2026

Proof of the singularity conjecture for discrete subgroups of $SL_{2} (R)$

Timothée Bénard

Let $μ$ be a finitely supported probability measure on $SL_{2} (R)$ whose support generates a Zariski-dense discrete subgroup. We prove that its stationary probabili…

math.DS2026

Classification of Choquet-Deny Lie groups

Timothée Bénard, Joshua Frisch

We characterize connected Lie groups on which all adapted random walks have only trivial bounded harmonic functions. In the nilpotent case, this answers a question of Furstenberg r…

math.DS2025

Khintchine dichotomy and Schmidt estimates for self-similar measures on $R^{d}$

Timothée Bénard, Weikun He, Han Zhang

We extend the classical theorems of Khintchine and Schmidt in metric Diophantine approximation to the context of self-similar measures on $R^{d}$ . For this, we establish eff…

math.PR2025

Noise stability on hyperbolic groups

Timothée Bénard, Ryokichi Tanaka

We show that symmetric random walks on non-elementary hyperbolic groups with non-zero homomorphisms into the reals are noise stable at linear scale under finite exponential moment…

math.DS2024

Khintchine dichotomy for self-similar measures

Timothée Bénard, Weikun He, Han Zhang

We establish the analogue of Khintchine's theorem for all self-similar probability measures on the real line. When specified to the case of the Hausdorff measure on the middle-thir…

math.DS2024★ 1 cited

Multislicing and effective equidistribution for random walks on some homogeneous spaces

Timothée Bénard, Weikun He

We consider a random walk on a homogeneous space $G /Λ$ where $G$ is $SO (2, 1)$ or $SO (3, 1)$ and $Λ$ is a lattice. The walk is driven by a probability measure $μ$ o…

math.PR2023

Local limit theorems for random walks on nilpotent Lie groups

Timothée Bénard, Emmanuel Breuillard

We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group $G$ , where the variables are allowed…

math.PR2023

The central limit theorem on nilpotent Lie groups

Timothée Bénard, Emmanuel Breuillard

We formulate and establish the central limit theorem for products of i.i.d. random variables on arbitrary simply connected nilpotent Lie groups, allowing a possible bias. Two new p…

math.DS2022

Winding of geodesic rays chosen by a harmonic measure

Timothée Bénard

We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain applications to the inverse problem…

math.DS2022

Exponential multiple mixing for commuting automorphisms of a nilmanifold

Timothée Bénard, Péter P. Varjú

Let $l \in N_{\geq 1}$ and $α : Z^{l} \to Aut (N)$ be an action of $Z^{l}$ by automorphisms on a compact nilmanifold $N$ . We a…

math.PR2021★ 1 cited

Equidistribution of mass for random processes on finite-volume spaces

Timothée Bénard

Let $G$ be a real Lie group, $Λ \subseteq G$ a lattice, and $X = G /Λ$ . We fix a probability measure $μ$ on $G$ and consider the left random walk induced on $X$ . It is assumed that $μ$ …

math.DS2021

Random walks with bounded first moment on finite-volume spaces

Timothée Bénard, Nicolas de Saxcé

Let $G$ be a real Lie group, $Λ \leq G$ a lattice, and $Ω = G /Λ$ . We study the equidistribution properties of the left random walk on $Ω$ induced by a probability measure $μ$ on $G$ .…

math.DS2021

Some asymptotic properties of random walks on homogeneous spaces

Timothée Bénard

Let $G$ be a connected semisimple real Lie group with finite center, and $μ$ a probability measure on $G$ whose support generates a Zariski-dense subgroup of $G$ . We consider the r…

math.DS2020

Drift of random walks on abelian covers of finite volume homogeneous spaces

Timothée Bénard

Let $G$ be a connected simple real Lie group, $Λ_{0} \subseteq G$ a lattice and $Λ ⊴ Λ_{0}$ a normal subgroup such that $Λ_{0} /Λ ≃ Z^{d}$ . We study the drift of a ran…

math.DS2020

Transience in law for symmetric random walks in infinite measure

Timothée Bénard

We consider a random walk on a second countable locally compact topological space endowed with an invariant Radon measure. We show that if the walk is symmetric and if every subset…

Proof of the singularity conjecture for discrete subgroups of SL2​(R)

Classification of Choquet-Deny Lie groups

Khintchine dichotomy and Schmidt estimates for self-similar measures on Rd

Noise stability on hyperbolic groups

Khintchine dichotomy for self-similar measures

Multislicing and effective equidistribution for random walks on some homogeneous spaces

Local limit theorems for random walks on nilpotent Lie groups

The central limit theorem on nilpotent Lie groups

Winding of geodesic rays chosen by a harmonic measure

Exponential multiple mixing for commuting automorphisms of a nilmanifold

Equidistribution of mass for random processes on finite-volume spaces

Random walks with bounded first moment on finite-volume spaces

Some asymptotic properties of random walks on homogeneous spaces

Drift of random walks on abelian covers of finite volume homogeneous spaces

Transience in law for symmetric random walks in infinite measure

Proof of the singularity conjecture for discrete subgroups of $SL_{2} (R)$

Khintchine dichotomy and Schmidt estimates for self-similar measures on $R^{d}$