An example of the rate of growth for a random walk on a group

Dyubina, Anna

doi:10.1070/rm1999v054n05abeh000208

Cited by 16 publications

(9 citation statements)

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“…Consider each of the three cases: m −1 < 0 n, n −1 and 0 m separately. 6 • The case m −1 < 0 n. If z n, then we have:…”

Section: The Wreath Products Of Groups With the Infinite Cyclic Groupmentioning

confidence: 99%

“…For wreath products there is an abundance of results on quantitative characteristics such as growth rate [18], isoperimetric profiles [11] and drift of simple random walks [6,10]. This makes studying representations of Cayley graphs of wreath products relevant to seeking connections between characteristics of groups and the computational power of automata that are sufficient to represent their Cayley graphs.…”

Section: Introductionmentioning

confidence: 99%

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Cayley Automatic Representations of Wreath Products

Berdinsky

Khoussainov

2016

Int. J. Found. Comput. Sci.

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We construct the representations of Cayley graphs of wreath products using finite automata, pushdown automata and nested stack automata. These representations are in accordance with the notion of Cayley automatic groups introduced by Kharlampovich, Khoussainov and Miasnikov and its extensions introduced by Elder and Taback. We obtain the upper and lower bounds for a length of an element of a wreath product in terms of the representations constructed.

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“…Consider each of the three cases: m −1 < 0 n, n −1 and 0 m separately. 6 • The case m −1 < 0 n. If z n, then we have:…”

Section: The Wreath Products Of Groups With the Infinite Cyclic Groupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cayley Automatic Representations of Wreath Products

Berdinsky

Khoussainov

2016

Int. J. Found. Comput. Sci.

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“…for any Abelian group) L(n) is asymptotically √ n. Until recently the existence problem for groups with intermediate growth rate of L(n) was open. First examples were found by the author in [3], [5]. In these examples L(n) ≍ n 1− 1 2 k (for any positive integer k) and L(n) ≍ n/ ln(n).…”

Section: Introductionmentioning

confidence: 99%

On drift and entropy growth for random walks on groups

Erschler¹

2003

Ann. Probab.

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“…See, e.g., [8,10,15]. Recall that u denotes the uniform probability measure on the symmetric generating set S * (by definition, S * contains the identity element).…”

Section: Entropy Upper Bounds Using λ Pg Upper Boundsmentioning

confidence: 99%

Random walks and isoperimetric profiles under moment conditions

Saloff‐Coste¹,

Zheng²

2016

Ann. Probab.

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Let G be a finitely generated group equipped with a finite symmetric generating set and the associated word length function | · |. We study the behavior of the probability of return for random walks driven by symmetric measures µ that are such that ρ(|x|)µ(x) < ∞ for increasing regularly varying or slowly varying functions ρ, for instance,ǫ , ǫ > 0. For this purpose we develop new relations between the isoperimetric profiles associated with different symmetric probability measures. These techniques allow us to obtain a sharp L 2 -version of Erschler's inequality concerning the Følner functions of wreath products. Examples and assorted applications are included.

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An example of the rate of growth for a random walk on a group

Cited by 16 publications

References 0 publications

Cayley Automatic Representations of Wreath Products

Cayley Automatic Representations of Wreath Products

On drift and entropy growth for random walks on groups

Random walks and isoperimetric profiles under moment conditions

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