Effective Density of Non-Degenerate Random Walks on Homogeneous Spaces

被引：0

作者：

Kim, Wooyeon ^{[1
]}

Kogler, Constantin ^{[2
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Univ Oxford, Math Inst, Radcliffe Observ Quarter, Woodstock Rd, Oxford OX2 6GG, England

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2024年 / 2024卷 / 11期

基金：

欧洲研究理事会;

关键词：

STATIONARY MEASURES; SPECTRAL GAP; LIE-GROUPS; SEMISIMPLE; INVARIANT; SUBGROUPS; BOUNDS;

D O I：

10.1093/imrn/rnae011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high dimension to effective equidistribution in the setting of random walks on homogeneous spaces, exploiting the spectral gap of the associated convolution operator.

引用

页码：9218 / 9236

页数：19

共 50 条

[31] ON NON-DEGENERATE PROBABILITY DISTRIBUTIONS IN 1P-SPACES
VAKHANIY.NN
THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1966, 11 (03): : 463 - &
[32] Aspects of convergence of random walks on finite volume homogeneous spaces
Prohaska, Roland
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2024, 39 (02): : 243 - 267
[33] Recurrence and ergodicity of random walks on linear groups and on homogeneous spaces
Guivarc'h, Y.
Raja, C. R. E.
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2012, 32 : 1313 - 1349
[34] Random generation of direct sums of finite non-degenerate subspaces
Glasby, Stephen P.
Niemeyer, Alice C.
Praeger, Cheryl E.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 649 : 408 - 432
[35] BROWNIAN TRANSITION FUNCTIONS + RANDOM WALKS ON CERTAIN HOMOGENEOUS SPACES
GANGOLLI, R
JOURNAL OF MATHEMATICS AND MECHANICS, 1964, 13 (04): : 603 - &
[36] MARKOV RANDOM WALKS ON HOMOGENEOUS SPACES AND DIOPHANTINE APPROXIMATION ON FRACTALS
Prohaska, Roland
Sert, Cagri
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 373 (11) : 8163 - 8196
[37] Random Walks in Degenerate Random Environments
Holmes, Mark
Salisbury, Thomas S.
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2014, 66 (05): : 1050 - 1077
[38] Non-degenerate homogeneous ∈-Kahler and ∈-quaternion Kahler structures of linear type
Lujan, Ignacio
Swann, Andrew
MONATSHEFTE FUR MATHEMATIK, 2015, 178 (01): : 113 - 142
[39] Invariance principle for non-homogeneous random walks
Georgiou, Nicholas
Mijatovic, Aleksandar
Wade, Andrew R.
ELECTRONIC JOURNAL OF PROBABILITY, 2019, 24
[40] Adiabatic approximation in the density matrix approach: non-degenerate systems
Pinto, ACA
Romero, KMF
Thomaz, MT
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2002, 311 (1-2) : 169 - 187

← 1 2 3 4 5 →