scholarly journals Random walks on the affine group of local fields and of homogeneous trees

1994 ◽  
Vol 44 (4) ◽  
pp. 1243-1288 ◽  
Author(s):  
Donald I. Cartwright ◽  
Vadim A. Kaimanovich ◽  
Wolfgang Woess
Keyword(s):  
Random Walks ◽  
Affine Group ◽  
Local Fields ◽  
Homogeneous Trees

Harmonic analysis for anisotropic random walks on homogeneous trees

1994 ◽  
Vol 110 (531) ◽  
pp. 0-0 ◽  
Author(s):  
Alessandro Figà-Talamanca ◽  
Tim Steger
Keyword(s):  
Random Walks ◽  
Harmonic Analysis ◽  
Homogeneous Trees

scholarly journals Brownian motion and finite approximations of quantum systems over local fields

2017 ◽  
Vol 29 (05) ◽  
pp. 1750016 ◽  
Author(s):  
Erik Makino Bakken ◽  
Trond Digernes ◽  
David Weisbart
Keyword(s):  
Brownian Motion ◽  
Random Walks ◽  
Local Field ◽  
Schrödinger Operators ◽  
Quantum Systems ◽  
Local Fields ◽  
Schrodinger Operators ◽  
Finite Systems ◽  
Finite Approximations ◽  
Finite Approximability

We give a stochastic proof of the finite approximability of a class of Schrödinger operators over a local field, thereby completing a program of establishing in a non-Archimedean setting corresponding results and methods from the Archimedean (real) setting. A key ingredient of our proof is to show that Brownian motion over a local field can be obtained as a limit of random walks over finite grids. Also, we prove a Feynman–Kac formula for the finite systems, and show that the propagator at the finite level converges to the propagator at the infinite level.

Anisotropic branching random walks on homogeneous trees

2000 ◽  
Vol 116 (1) ◽  
pp. 57-88 ◽  
Author(s):  
Irene Hueter ◽  
Steven P. Lalley
Keyword(s):  
Random Walks ◽  
Branching Random Walks ◽  
Homogeneous Trees

scholarly journals Random walks on the discrete affine group

2021 ◽  
Author(s):  
Jérémie Brieussel ◽  
Ryokichi Tanaka ◽  
Tianyi Zheng
Keyword(s):  
Random Walks ◽  
Affine Group

scholarly journals Large Deviations for Radial Random Walks on Homogeneous Trees

2007 ◽  
Vol 187 ◽  
pp. 75-90
Author(s):  
Kanji Ichihara
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Large Deviations ◽  
Random Walks ◽  
Large Deviation ◽  
Rate Function ◽  
Homogeneous Tree ◽  
Homogeneous Trees ◽  
Radial Random Walks

AbstractDonsker-Varadhan’s type large deviation will be discussed for the pinned motion of a radial random walk on a homogeneous tree. We shall prove that the rate function corresponding to the large deviation is associated with a new Markov chain constructed from the above random walk through a harmonic transform based on a positive principal eigenfunction for the generator of the random walk.

scholarly journals Recurrence and ergodicity of random walks on linear groups and on homogeneous spaces

2011 ◽  
Vol 32 (4) ◽  
pp. 1313-1349 ◽  
Author(s):  
Y. GUIVARC’H ◽  
C. R. E. RAJA
Keyword(s):  
Random Walks ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Local Fields ◽  
Quadratic Growth ◽  
Linear Groups ◽  
Compact Groups ◽  
Large Classes ◽  
Skew Products ◽  
Recurrent Random Walk

AbstractWe discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular, we show that a closed subgroup of a product of finitely many linear groups over local fields supports an adapted recurrent random walk if and only if it has at most quadratic growth. We give also a detailed analysis of ergodicity properties for special classes of random walks on homogeneous spaces and for associated homeomorphisms with infinite invariant measure. The structural properties of closed subgroups of linear groups over local fields and the properties of group actions with respect to certain Radon measures associated with random walks play an important role in the proofs.

Non-homogeneous Random Walks

2016 ◽  
Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Andrew Wade
Keyword(s):  
Random Walks
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