Small spectral radius and percolation constants on non-amenable Cayley graphs

Autor:	Kate Juschenko, Tatiana Nagnibeda
Rok vydání:	2015
Předmět:	Spectral radius General Mathematics Astrophysics::High Energy Astrophysical Phenomena Group Theory (math.GR) 01 natural sciences Condensed Matter::Disordered Systems and Neural Networks Cayley graph Combinatorics 010104 statistics & probability Mathematics::Probability FOS: Mathematics 0101 mathematics Mathematics Discrete mathematics spectral radius Conjecture Group (mathematics) Applied Mathematics 010102 general mathematics Bernoulli percolation Non-amenable group Percolation Generating set of a group Condensed Matter::Statistical Mechanics isoperimetric constant Multiple edges Isoperimetric inequality Mathematics - Group Theory
Zdroj:	Proc. Amer. Math. Soc. Proceedings AMS
Popis:	Motivated by the Benjamini-Schramm non-unicity of percolation conjecture we study the following question. For a given finitely generated non-amenable group $\Gamma$, does there exist a generating set $S$ such that the Cayley graph $(\Gamma,S)$, without loops and multiple edges, has non-unique percolation, i.e., $p_c(\Gamma,S)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb3efd1d77b20f0a121a6dd5ece001fd http://arxiv.org/abs/1206.2183 Zobrazit plný text záznamu