7 papers
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…
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…
measure equivalence of nilpotent groups
Thiebout Delabie, Claudio Llosa Isenrich, Romain Tessera
We classify compactly generated locally compact groups of polynomial growth up to measure equivalence (ME) for all . To achieve this, we combine rigidity results (pr…
On the stability of hyperbolicity under quantitative measure equivalence
Thiebout Delabie, Juhani Koivisto, François Le Maître +1
A well-known result of Shalom says that lattices in SO are measure equivalent for all . His proof actually yields the following stronger statement: the…
Balls in groups: volume, structure and growth
Romain Tessera, Matthew Tointon
We develop a fine-scale structural theory for balls of polynomial volume in finitely generated groups. Our main result shows that a polynomial-volume hypothesis on a single ball im…
Small doubling implies small tripling for balls of large radius
Romain Tessera, Matthew Tointon
We show that if is a parameter and is a finite symmetric subset of a group containing the identity such for some integer , then $|S^{3n}|…
Algebraically recurrent random walks on groups
Itai Benjamini, Hilary Finucane, Romain Tessera
Initial steps are presented towards understanding which finitely generated groups are almost surely generated as semigroups by the path of a random walk on the group.