On the stability of the behavior of random walks on groups

By C. Pittet, Laurent Saloff-Coste. 2000

92 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc8f9479c1fa0fc9b80ed8e69b7ee5f15dfd3b9f

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On amenability of automata groups (2008, background): “o a ﬁnite extension (see [PSC99]), the return proﬁle of the wreath product M(X) ≀ Sym(X) satisﬁes this inequality as well. Further, by the monotonicity of the return proﬁle under passing to subgroups [PSC00], the same inequality from Theorem 4.13 is also satisﬁed for the return proﬁle of an arbitrar”
On symmetric random walks with random conductances on ℤd (2004, background): “The proof is based on a trace formula (in fact an extension of the trace formula for central probability for random walks on amenable groups, see [9]).”
Poisson-Furstenberg Boundaries, Large-scale Geometry and Growth of Groups (2011, background): “This implies that for this (and hence also for any other simple random walk, see Pittet, Saloff-Coste [76]) on any Grigorchuk group, the probability to return to the origin satisfies pn(e, e) ≤ exp(−Cn1/2).”
Random walks on finite rank solvable groups (2003, background): “See [20] for the proofs of these stability properties.”
ON RANDOM WALKS ON WREATH PRODUCTS (2002, background): “The condition that q has finite support can be relaxed to ∑ x∈G |x|2q(x) <∞, where |x| is the graph distance on (G,S) (see [40] and [51]).”
A geometric approach to on-diagonal heat kernel lower bounds on groups (2001, methodology): “Note that the behavior of ΦM(t) for large t does not depend on the choice of the Riemannian structure up to multiplicative constants (see [47], [34]).”
Speed of random walks, isoperimetry and compression of finitely generated groups (2015, background): “The ℓp-isoperimetric proﬁles and return probability associated with symmetric probability measures of ﬁnite generating support are also known to be stable under quasi-isometry, see Pittet-Saloﬀ-Coste [PSC00], but it is an open question regarding speed and entropy. Denote f(x) ≃Cg(x) if 1 Cg(x) ≤ f(x”
Processes on Unimodular Random Networks (2006, background): “Pittet and Saloff-Coste (2000), Lemma 3.1, prove an analogous comparison result for Cayley graphs, but with different assumptions on the pairs of rates (which are deterministic for them).”