scholarly journals Potential theory of random walks on Abelian groups

1969 ◽  
Vol 122 (0) ◽  
pp. 19-114 ◽  
Author(s):  
Sidney C. Port ◽  
Charles J. Stone
Keyword(s):  
Random Walks ◽  
Potential Theory ◽  
Abelian Groups

Potential Theory on Distance-Regular Graphs

1993 ◽  
Vol 2 (3) ◽  
pp. 243-255 ◽  
Author(s):  
Norman L. Biggs
Keyword(s):  
Random Walks ◽  
Potential Theory ◽  
Effective Resistance ◽  
Electrical Network ◽  
Regular Graphs ◽  
Regular Case ◽  
Explicit Formulae ◽  
Distance Regular Graphs ◽  
A Current

A graph may be regarded as an electrical network in which each edge has unit resistance. We obtain explicit formulae for the effective resistance of the network when a current enters at one vertex and leaves at another in the distance-regular case. A well-known link with random walks motivates a conjecture about the maximum effective resistance. Arguments are given that point to the truth of the conjecture for all known distance-regular graphs.

scholarly journals Law of large numbers for the drift of the two-dimensional wreath product

2021 ◽  
Author(s):  
Anna Erschler ◽  
Tianyi Zheng
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Wreath Product ◽  
Law Of Large Numbers ◽  
Abelian Groups ◽  
Limiting Distribution ◽  
Two Dimensional ◽  
Lamplighter Group ◽  
Large Numbers ◽  
Asymptotic Geometry

AbstractWe prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite $$(2+\epsilon )$$ ( 2 + ϵ ) -moment. This result is in contrast with classical examples of abelian groups, where the displacement after n steps, normalised by its mean, does not concentrate, and the limiting distribution of the normalised n-step displacement admits a density whose support is $$[0,\infty )$$ [ 0 , ∞ ) . We study further examples of groups, some with random walks satisfying LLN for drift and other examples where such concentration phenomenon does not hold, and study relation of this property with asymptotic geometry of groups.

scholarly journals CLT for Random Walks of Commuting Endomorphisms on Compact Abelian Groups

2015 ◽  
Vol 30 (1) ◽  
pp. 143-195 ◽  
Author(s):  
Guy Cohen ◽  
Jean-Pierre Conze
Keyword(s):  
Random Walks ◽  
Abelian Groups ◽  
Compact Abelian Groups

scholarly journals Recurrence criteria for random walks on countable Abelian groups

1974 ◽  
Vol 18 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Leopold Flatto ◽  
Joel Pitt
Keyword(s):  
Random Walks ◽  
Abelian Groups

scholarly journals Long time behavior of random walks on abelian groups

2010 ◽  
Vol 118 (2) ◽  
pp. 445-464
Author(s):  
Alexander Bendikov ◽  
Barbara Bobikau
Keyword(s):  
Random Walks ◽  
Abelian Groups ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time
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