Random Walks on Infinite Graphs and Groups: Bibliography

By Wolfgang Woess. 2000

937 citations recorded by the source corpus.

Subfields: History, Literature and Literary Theory, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/9321863a611efeb36bbe71991c68984ff56ba5be

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Citations in the corpus

Asymptotic entropy and Green speed for random walks on countable groups (2006, neutral): “This assumption is always satisﬁed if Γ is not a ﬁnite extension of Z or Z 2 (see Woess [25, Sect.”
Connected Lie groups and property RD (2004, background): “The authors observed [4] that property RD is also relevant to the study of the asymptotic behavior of the probability of return of random walks on non-amenable groups (for a general reference on random walks, see [36]).”
Milnor's Problem on the Growth of Groups and its Consequences (2011, background): “Woess [225], the paper of Kaimanovich and Vershik [136], the article [32], and the unfinished manuscript “A survey on the relationships between volume growth, isoperimetry, and the behavior of simple random walk on Cayley graphs, with examples” of C.”
Random Walks on Trees with Finitely Many Cone Types (2002, methodology): “We now apply a method that we have learnt from the paper of Lalley (1993) and which is exposed in detail in Woess (2000), Section 19. It has also been used in other branches of mathematics, see e.g., Hersonsky and Hubbard (1997), Drmota (1997).”
The critical Branching Markov Chain is transient (2005, neutral): “The spectral radius can be calculated with the help of the Perron-Frobenius Theorem (see for example [8]):”
Graph Laplacians and their Convergence on Random Neighborhood Graphs (2006, methodology): “and therefore can be used to define a Markov random walk on V , see for example Woess (2000) .”
Variance decay for functionals of the environment viewed by the particle (2009, background): “The second part of the lemma is due to [1] (see also [25], Lemma 2.”
Buildings and Hecke algebras (2006, background): “This is easily seen to be independent of x ∈ X, by irreducibility (see [45]).”
Random walk in random groups (2003, background): “In other words, En(f) is asymptotic to Eμm(f) for n = 2k−2 2k m that agrees with the law of large numbers saying that most of the measure μn(id →) is contained near the sphere of radius r = n(2k−2) 2k , where “near” refers to the band of width O( √ r) (compare [Wo]).”