Introduction to random walks on homogeneous spaces

被引：14

作者：

Benoist, Yves ^{[1
]}

Quint, Jean-Francois ^{[2
]}

机构：

[1] Univ Paris 11, Dept Math, Ctr Natl Rech Sci, F-91405 Orsay, France

[2] Univ Paris 13, LAGA, Ctr Natl Rech Sci, F-93430 Villetaneuse, France

来源：

JAPANESE JOURNAL OF MATHEMATICS | 2012年 / 7卷 / 02期

关键词：

Lie groups; discrete subgroups; homogeneous dynamics; random walk; INVARIANT-MEASURES; UNIPOTENT FLOWS; TORAL AUTOMORPHISMS; HECKE POINTS; EQUIDISTRIBUTION; CONVERGENCE; CONJECTURE; PRODUCTS; THEOREMS; ORBITS;

D O I：

10.1007/s11537-012-1220-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let a (0) and a (1) be two matrices in SL(2, ) which span a non-solvable group. Let x (0) be an irrational point on the torus . We toss a (0) or a (1), apply it to x (0), get another irrational point x (1), do it again to x (1), get a point x (2), and again. This random trajectory is equidistributed on the torus. This phenomenon is quite general on any finite volume homogeneous space.

引用

页码：135 / 166

页数：32

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