The martin boundary for general isotropic random walks in a tree

1991 ◽  
Vol 4 (1) ◽  
pp. 111-136 ◽  
Author(s):  
Donald I. Cartwright ◽  
Stanley Sawyer
Keyword(s):  
Random Walks ◽  
Martin Boundary ◽  
Isotropic Random

scholarly journals Limit theorems for isotropic random walks on triangle buildings

2002 ◽  
Vol 73 (3) ◽  
pp. 301-334 ◽  
Author(s):  
Marc Lindlbauer ◽  
Michael Voit
Keyword(s):  
Limit Theorem ◽  
Random Walks ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Two Dimensional ◽  
Littlewood Polynomials ◽  
Large Numbers ◽  
Moment Functions ◽  
Vertex Sets ◽  
Isotropic Random

AbstractThe spherical functions of triangle buildings can be described in terms of certain two-dimensional orthogonal polynomials on Steiner's hypocycloid which are closely related to Hall-Littlewood polynomials. They lead to a one-parameter family of two-dimensional polynimial hypergroups. In this paper we investigate isotropic random walks on the vertex sets of triangle buildings in terms of their projections to these hypergroups. We present strong laws of large numbers, a central limit theorem, and a local limit theorem; all these results are well-known for homogeneous trees. Proofs are based on moment functions on hypergroups and on explicit expansions of the hypergroup characters in terms of certain two-dimensional Tchebychev polynimials.

Isotropic random walks in a building of type

2004 ◽  
Vol 247 (1) ◽  
pp. 101-135 ◽  
Author(s):  
Donald I. Cartwright ◽  
Wolfgang Woess
Keyword(s):  
Random Walks ◽  
Isotropic Random

scholarly journals Exit laws from large balls of (an)isotropic random walks in random environment

2015 ◽  
Vol 43 (6) ◽  
pp. 2859-2948 ◽  
Author(s):  
Erich Baur ◽  
Erwin Bolthausen
Keyword(s):  
Random Walks ◽  
Random Environment ◽  
Isotropic Random
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