%0 Conference Proceedings
%T A Characterization of Amenable Groups by Besicovitch Pseudodistances
%+ Institute of Cybernetics [Tallinn]
%+ Institut de Mathématiques de Marseille (I2M)
%+ Laboratoire Cogitamus = Cogitamus Laboratory
%A Capobianco, Silvio
%A Guillon, Pierre
%A Noûs, Camille
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 26th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA)
%C Stockholm, Sweden
%Y Hector Zenil
%I Springer International Publishing
%3 Cellular Automata and Discrete Complex Systems
%V LNCS-12286
%P 99-110
%8 2020-08-10
%D 2020
%R 10.1007/978-3-030-61588-8_8
%K Besicovitch distance
%K Følner sequences
%K Submeasures
%K Amenability
%K Non-Compact space
%K Symbolic dynamics
%Z Mathématiques [math]/Topologie générale [math.GN] Mathématiques [math]/Théorie des groupes [math.GR] Mathématiques [math]/Systèmes dynamiques [math.DS]
%Z Computer Science [cs]
%Z Computer Science [cs]/Other [cs.OH]Conference papers
%X The Besicovitch pseudodistance defined in [BFK99] for one-dimensional configurations is invariant by translations. We generalize the definition to arbitrary countable groups and study how properties of the pseudodistance, including invariance by translations, are determined by those of the sequence of finite sets used to define it. In particular, we recover that if the Besicovitch pseudodistance comes from a nondecreasing exhaustive Følner sequence, then every shift is an isometry. For non-Følner sequences we prove that some shifts are not isometries, and the Besicovitch pseudodistance with respect to some subsequence even makes them non-continuous.
%G English
%Z TC 1
%Z WG 1.5
%2 https://hal.science/hal-03100934/document
%2 https://hal.science/hal-03100934/file/496967_1_En_8_Chapter.pdf
%L hal-03100934
%U https://hal.science/hal-03100934
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-AUTOMATA
%~ IFIP-LNCS-12286