Subshifts with slow complexity and simple groups with the Liouville property

Autor:	Nicolás Matte Bon
Rok vydání:	2014
Předmět:	Discrete mathematics Stallings theorem about ends of groups Simple (abstract algebra) Group (mathematics) Simple group Boundary (topology) Geometry and Topology Complexity function Random walk Analysis Probability measure Mathematics
Zdroj:	Geometric and Functional Analysis. 24:1637-1659
ISSN:	1420-8970 1016-443X
DOI:	10.1007/s00039-014-0293-4
Popis:	We study random walk on topological full groups of subshifts, and show the existence of infinite, finitely generated, simple groups with the Liouville property. Results by Matui and Juschenko-Monod have shown that the derived subgroups of topological full groups of minimal subshifts provide the first examples of finitely generated, simple amenable groups. We show that if the (not necessarily minimal) subshift has a complexity function that grows slowly enough (e.g. linearly), then every symmetric and finitely supported probability measure on the topological full group has trivial Poisson–Furstenberg boundary. We also get explicit upper bounds for the growth of Folner sets.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::03c525d370897ca38899cc6808c07938 https://doi.org/10.1007/s00039-014-0293-4 Zobrazit plný text záznamu Full text from SpringerLink