ON THE SPECTRUM AND MARTIN BOUNDARY OF HOMOGENEOUS SPACES

被引：0

作者：

NORTHSHIELD, S ^{[1
]}

机构：

[1] SUNY COLL PLATTSBURGH,DEPT MATH,PLATTSBURGH,NY 12901

来源：

STATISTICS & PROBABILITY LETTERS | 1995年 / 22卷 / 04期

关键词：

HOMOGENEOUS SPACE; MARKOV PROCESS; SPECTRUM; MARTIN BOUNDARY; FIXED POINT; AMENABLE GROUP;

D O I：

10.1016/0167-7152(94)00077-L

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Given a conservative, spatially homogeneous Markov process X on an homogeneous spaces X, we show that if the bottom of the spectrum of the generator of X is zero then the Martin boundary of X contains a unique point fixed by the isometry group of X.

引用

页码：275 / 279

页数：5

共 9 条

[1] ALDOUS D, 1990, COMMUNICATION
[2] Brelot M., 1971, TOPOLOGIES BOUNDARIE
[3] Chavel I., 1984, EIGENVALUES RIEMANNI
[4] THE STRUCTURE OF COMPLETE STABLE MINIMAL-SURFACES IN 3-MANIFOLDS OF NONNEGATIVE SCALAR CURVATURE
FISCHERCOLBRIE, D
SCHOEN, R
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (02) : 199 - 211
[5] ITO K, 1984, LECTURES STOCHASTIC
[6] LOEB P. A., 1965, ANN I FOURIER, V15, P597
[7] LYONS T, 1984, J DIFFER GEOM, V19, P299
[8] NORTHSHIELD S, 1992, P AM MATH SOC, V119, P561
[9] PETERSON ALT, 1988, AMENABILITY

← 1 →