Romain Tessera

collaborators

5 papers

math.PR2026

Concentration inequalities for maximal displacement of random walks on groups of polynomial growth

JÃ©rÃ©mie 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…

math.CO2025

Small doubling implies small tripling for balls of large radius

Romain Tessera, Matthew Tointon

We show that if $K \geq 1$ is a parameter and $S$ is a finite symmetric subset of a group containing the identity such $∣ S^{2 n} ∣ \leq K ∣ S^{n} ∣$ for some integer $n \geq 2 K^{2}$ , then $|S^{3n}|…

math.GR2025

Measure equivalence and sofic approximations

Thiebout Delabie, Juhani Koivisto, Romain Tessera

We introduce a technique for producing a measure coupling between two sofic groups from a family of maps between their sofic approximations. We exploit this to construct measure co…

math.GR2025

On the stability of hyperbolicity under quantitative measure equivalence

Thiebout Delabie, Juhani Koivisto, FranÃ§ois Le MaÃ®tre +1

A well-known result of Shalom says that lattices in SO $(n, 1)$ are $L^{p}$ measure equivalent for all $p < n - 1$ . His proof actually yields the following stronger statement: the…

math.GR2025

$L^{p}$ measure equivalence of nilpotent groups

Thiebout Delabie, Claudio Llosa Isenrich, Romain Tessera

We classify compactly generated locally compact groups of polynomial growth up to $L^{p}$ measure equivalence (ME) for all $p \leq 1$ . To achieve this, we combine rigidity results (pr…

Concentration inequalities for maximal displacement of random walks on groups of polynomial growth

Small doubling implies small tripling for balls of large radius

Measure equivalence and sofic approximations

On the stability of hyperbolicity under quantitative measure equivalence

Lp measure equivalence of nilpotent groups

$L^{p}$ measure equivalence of nilpotent groups