Quasimorphisms, random walks, and transient subsets in countable groups

Standard

Quasimorphisms, random walks, and transient subsets in countable groups. / Malyutin, A. V.

In: Journal of Mathematical Sciences , Vol. 181, No. 6, 01.03.2012, p. 871-885.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{7142826d85644789884a22b23f52d735,

title = "Quasimorphisms, random walks, and transient subsets in countable groups",

abstract = "We study the interrelations between the theory of quasimorphisms and the theory of random walks on groups, and establish the following transience criterion for subsets of groups: if a subset of a countable group has bounded images under any three linearly independent homogeneous quasimorphisms on the group, the this subset is transient for all nondegenerate random walks on the group. From this it follows, by results of M. Bestvina, K. Fujiwara, J. Birman, W. Menasco, and others, that, in a certain sense, generic elements in the mapping class groups of surfaces are pseudo-Anosov, generic braids in Artin's braid groups represent prime links and knots, generic elements in the commutant of every nonelementary hyperbolic group have large stable commutator length, etc. Bibliography: 20 titles.",

author = "Malyutin, {A. V.}",

year = "2012",

month = mar,

day = "1",

doi = "10.1007/s10958-012-0721-7",

language = "русский",

volume = "181",

pages = "871--885",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - Quasimorphisms, random walks, and transient subsets in countable groups

AU - Malyutin, A. V.

PY - 2012/3/1

Y1 - 2012/3/1

N2 - We study the interrelations between the theory of quasimorphisms and the theory of random walks on groups, and establish the following transience criterion for subsets of groups: if a subset of a countable group has bounded images under any three linearly independent homogeneous quasimorphisms on the group, the this subset is transient for all nondegenerate random walks on the group. From this it follows, by results of M. Bestvina, K. Fujiwara, J. Birman, W. Menasco, and others, that, in a certain sense, generic elements in the mapping class groups of surfaces are pseudo-Anosov, generic braids in Artin's braid groups represent prime links and knots, generic elements in the commutant of every nonelementary hyperbolic group have large stable commutator length, etc. Bibliography: 20 titles.

AB - We study the interrelations between the theory of quasimorphisms and the theory of random walks on groups, and establish the following transience criterion for subsets of groups: if a subset of a countable group has bounded images under any three linearly independent homogeneous quasimorphisms on the group, the this subset is transient for all nondegenerate random walks on the group. From this it follows, by results of M. Bestvina, K. Fujiwara, J. Birman, W. Menasco, and others, that, in a certain sense, generic elements in the mapping class groups of surfaces are pseudo-Anosov, generic braids in Artin's braid groups represent prime links and knots, generic elements in the commutant of every nonelementary hyperbolic group have large stable commutator length, etc. Bibliography: 20 titles.

UR - http://www.scopus.com/inward/record.url?scp=84858750764&partnerID=8YFLogxK

U2 - 10.1007/s10958-012-0721-7

DO - 10.1007/s10958-012-0721-7

M3 - статья

AN - SCOPUS:84858750764

VL - 181

SP - 871

EP - 885

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 47487700