Lp compression, traveling salesmen, and stable walks

By Assaf Naor, Yuval Peres. 2009

51 citations recorded by the source corpus.

We show that if H is a group of polynomial growth whose growth rate is at least quadratic then the Lp compression of the wreath product Z oH equals max { 1 p , 1 2 } . We also show that the Lp compression of Z oZ equals max { p 2p−1 , 2 3 } and the Lp compression of (Z oZ)0 (the zero section of Z oZ, equipped with the metric induced from Z o Z) equals max { p+1 2p , 3 4 } . The fact that the Hilbert compression exponent of Z o Z equals 3 while the Hilbert compression exponent of (Z o Z)0 equals 3 4 is used to show that there exists a Lipschitz function f : (Z o Z)0 → L2 which cannot be extended to a Lipschitz function defined on all of Z o Z.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/75a030386139ffa38aa97a0e06885a3b5163eb5d

Citations in the corpus

• Speed of random walks, isoperimetry and compression of finitely generated groups (2015, unknown): “1093/imrn/rnn076 [68] Naor, Assaf; Peres, Yuval, {\(L_p\)} compression, traveling salesmen, and stable walks, Duke Math.”