72 citations · 401 across the 40 of their papers we have counts for
6 papers · 1 filter
On the failure of concentration for the \ell_\infty-ball
Tim Austin
Let be a compact metric space and a Borel probability on . For each let be the -product on of copies of , and consider $…
Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces
Tim Austin, Assaf Naor, Romain Tessera
Let $\H$ denote the discrete Heisenberg group, equipped with a word metric associated to some finite symmetric generating set. We show that if is a -convex…
A finitely-generated amenable group with very poor compression into Lebesgue spaces
Tim Austin
We construct an example of a finitely-generated amenable group that does not admit any coarse 1-Lipschitz embedding with positive compression exponent into L_p for any 1 \leq p < \…
The wreath product of Z with Z has Hilbert compression exponent 2/3
Tim Austin, Assaf Naor, Yuval Peres
Let G be a finitely generated group, equipped with the word metric d associated with some finite set of generators. The Hilbert compression exponent of G is the supremum over all $…
The Euclidean distortion of the lamplighter group
Tim Austin, Assaf Naor, Alain Valette
We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion . This matches the lower bound proved by Lee, Naor and Pe…
On contractive families and a fixed-point question of Stein
Tim D. Austin
In this paper we disprove the following conjectured generalization of the Contraction Mapping Theorem (due to J.D. Stein Jr.): Let X be a complete metric space and let F be a finit…