Pathological Topologies and Random Walks on Abelian Groups

2010 ◽  
pp. 425-432
Author(s):  
R. M. Dudley
Keyword(s):  
Random Walks ◽  
Abelian Groups

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 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

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

scholarly journals Recurrent Random Walks on Countable Abelian Groups of Rank 2

1975 ◽  
Vol 3 (2) ◽  
pp. 380-386
Author(s):  
Leopold Flatto ◽  
Joel Pitt
Keyword(s):  
Random Walks ◽  
Abelian Groups ◽  
Rank 2

scholarly journals Random walks on abelian groups

1962 ◽  
Vol 13 (3) ◽  
pp. 447-447 ◽  
Author(s):  
R. M. Dudley
Keyword(s):  
Random Walks ◽  
Abelian Groups

scholarly journals Random walks on discrete Abelian groups

2018 ◽  
Vol 152 (2) ◽  
pp. 273-284
Author(s):  
Margaryta Myronyuk
Keyword(s):  
Random Walks ◽  
Abelian Groups
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