181 citations · 480 across the 16 of their papers we have counts for
5 papers · 1 filter
Embeddings of discrete groups and the speed of random walks
Assaf Naor, Yuval Peres
For a finitely generated group G and a banach space X let α^*_X(G) (respectively α^#_X(G)) be the supremum over all α\ge 0 such that there exists a Lipschitz mapping (respectively…
The two possible values of the chromatic number of a random graph
Dimitris Achlioptas, Assaf Naor
Given d \in (0,infty) let k_d be the smallest integer k such that d < 2k\log k. We prove that the chromatic number of a random graph G(n,d/n) is either k_d or k_d+1 almost surely.
Trees and Markov convexity
James R. Lee, Assaf Naor, Yuval Peres
We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly…
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…