The measurable Kesten theorem Academic Article uri icon


  • 1. Introduction. Let G be a d-regular, finite or infinite connected undirected graph. Let M be the Markov averaging operator on l2(G). When G is infinite, we define the spectral radius of G, denoted ρ(G), to be the norm of M. When G is finite, we want to exclude the trivial eigenvalues, and thus define ρ(G) to be the second largest element in the set of absolute values of eigenvalues of M. For an infinite graph G, we have ρ(G) ≥ ρ(Td) = 2 … Received February 2012; revised May 2014. 1Supported in part by MTA Renyi “Lendulet” Groups and Graphs Research Group. 2Supported in part by ISF Grant 441/11 and US NSF Grants DMS-11-07452, 11-07263, 11-07367 “RNMS: Geometric structures And Representation varieties” (the GEAR Network). 3Supported by the NSERC Discovery Accelerator Grant and the Canada Research Chair program. MSC2010 subject classifications. Primary 05C81, 60G50; secondary 82C41. Key words and …

publication date

  • January 1, 2016