Stability of probability of return on locally compact groups under quasi-isometry

被引：0

作者：

Mohammed, Barmaki ^{[1
]}

Mostafa, Ftouhi ^{[1
]}

Gretete, Driss ^{[1
]}

机构：

[1] Univ Ibn Tofail, Dept Math Logist & IT, Kenitra, Morocco

来源：

ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES | 2021年 / 48卷 / 01期

关键词：

Probability of return; amenable group; locally compact; quasi-isometry; random walk; RANDOM-WALKS; BEHAVIOR;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this article is to demonstrate the invariance of the probability of return to the origin on the locally compact groups by quasi isometrics. This is a generalization of a theorem of Ch. Pittet and L. Salof-Coste (see [1]) who established this invariance in the case of discrete groups finitely generated.

引用

页码：32 / 36

页数：5

共 13 条

[1] RANDOM WALKS DRIVEN BY LOW MOMENT MEASURES [J].

Bendikov, Alexander ;

Saloff-Coste, Laurent .

ANNALS OF PROBABILITY, 2012, 40 (06) :2539-2588

[2]

Cartan H, 1940, CR HEBD ACAD SCI, V211, P759

[3]

Cornulier Y, 2016, EMS TRACTS MATH, V25, P1, DOI 10.4171/166

[4] Boundary behavior for groups of subexponential growth [J].

Erschler, A .

ANNALS OF MATHEMATICS, 2004, 160 (03) :1183-1210

[5] Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks [J].

Erschler, Anna .

PROBABILITY THEORY AND RELATED FIELDS, 2006, 136 (04) :560-586

[6] Stability of behaviour of random walks on locally compact groups [J].

Gretete, Driss .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2008, 44 (01) :129-142

[7] Random walk on a discrete Heisenberg group [J].

Gretete D. .

Rendiconti del Circolo Matematico di Palermo, 2011, 60 (3) :329-335

[8]

Kesten H, 1959, Trans. Amer. Math. Soc., V92, P336, DOI [10.1090/S0002-9947-1959-0109367-6, DOI 10.1090/S0002-9947-1959-0109367-6]

[9] Lower bounds for the random walks on amenable p-adic groups [J].

Mustapha, S .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2006, 42 (01) :81-88

[10] Random walks on finite rank solvable groups [J].

Pittet, C ;

Saloff-Coste, L .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2003, 5 (04) :313-342

← 1 2 →