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An abramov formula for stationary spaces of discrete groups, arXiv preprint arXiv:1204.5414
, 2012
"... Abstract. Let (G, µ) be a discrete group equipped with a generating probability measure, and let Γ be a finite index subgroup of G. A µrandom walk on G, starting from the identity, returns to Γ with probability one. Let θ be the hitting measure, or the distribution of the position in which the rand ..."
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Cited by 6 (1 self)
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Abstract. Let (G, µ) be a discrete group equipped with a generating probability measure, and let Γ be a finite index subgroup of G. A µrandom walk on G, starting from the identity, returns to Γ with probability one. Let θ be the hitting measure, or the distribution of the position in which the random walk first hits Γ. We prove that the Furstenberg entropy of a (G, µ)stationary space, with respect to the action of (Γ, θ), is equal to the Furstenberg entropy with respect to the action of (G, µ), times the index of Γ in G. The index is shown to be equal to the expected return time to Γ. As a corollary, when applied to the FurstenbergPoisson boundary of (G, µ), we prove that the random walk entropy of (Γ, θ) is equal to the random walk entropy of (G, µ), times the index of Γ in G.
unknown title
, 2009
"... This paper introduces Markov chains and processes over nonabelian free groups and semigroups. We prove a formula for the finvariant of a Markov chain over a free group in terms of transition matrices that parallels the classical formula for the entropy a Markov chain. Applications include free grou ..."
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group analogues of the AbramovRohlin formula for skewproduct actions and Yuzvinskii’s addition formula for algebraic actions. 1 Nonabelian free group actions: Markov processes, the AbramovRohlin formula and Yuzvinskii’s formula
Greatest Factorial Factorization and Symbolic Summation
 J. SYMBOLIC COMPUT
, 1995
"... This paper is selfcontained, no difference field knowledge but only basic facts from algebra are required. In the following we briefly review its sections. Section 2 presents the basic GFF notions, in particular the Fundamental Lemma and an algorithm for computing the GFFform of a polynomial. In S ..."
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Cited by 66 (7 self)
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. In Section 3 we investigate the relation to the dispersion function (Abramov, 1971) and discuss "shiftsaturated" polynomials which are polynomials with sufficiently nice GFFform. Due to lattice properties of K[x] with respect to gcd, a minimal shiftsaturated polynomial sat(p) can be assigned
Nonabelian free group actions: Markov . . .
, 2009
"... In previous work, a measureconjugacy invariant (called the finvariant) for actions of free groups was introduced. It is analogous to the KolmogorovSinai entropy. In this paper, analogues of the classical AbramovRohlin formula for skewproduct actions and Yuzvinskii’s addition formula for algebra ..."
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Cited by 10 (5 self)
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In previous work, a measureconjugacy invariant (called the finvariant) for actions of free groups was introduced. It is analogous to the KolmogorovSinai entropy. In this paper, analogues of the classical AbramovRohlin formula for skewproduct actions and Yuzvinskii’s addition formula
On the number of refusals in a busy period
 Probab. Engin. Inform. Sci
, 1999
"... Formulas are derived for moments of the number of refused customers in a busy period for the M0GI010n and the GI0M010n queueing systems+ As an interesting special case for the M0GI010n system, we note that the mean number is 1 when the mean interarrival time equals the mean service time+ This provid ..."
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Cited by 2 (0 self)
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Formulas are derived for moments of the number of refused customers in a busy period for the M0GI010n and the GI0M010n queueing systems+ As an interesting special case for the M0GI010n system, we note that the mean number is 1 when the mean interarrival time equals the mean service time
Entropy theory from the orbital point of view
 Monatsh. Math
"... Abstract. Inspired by [RW], we develop an orbital approach to the entropy theory for actions of countable amenable groups. This is applied to extend—with new short proofs—the recent results about uniform mixing of actions with completely positive entropy [RW], Pinsker factors and the relative disjoi ..."
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Cited by 16 (0 self)
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disjointness problems [GTW], AbramovRokhlin entropy addition formula [ZW], etc. Unlike the cited papers our work is independent of the standard machinery developed by OrnsteinWeiss [OW] or Kieffer [Ki]. We do not use nonorbital tools like Rokhlin lemma, ShannonMcMillan theorem, castle analysis, joining
Entropy geometry and disjointness for zerodimensional algebraic actions
 J. Reine Angew. Math
, 2005
"... Abstract. We show that many algebraic actions of higherrank abelian groups on zerodimensional groups are mutually disjoint. The proofs exploit differences in the entropy geometry arising from subdynamics and a form of Abramov–Rokhlin formula for halfspace entropies. We discuss some mutual disjoint ..."
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Cited by 7 (2 self)
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Abstract. We show that many algebraic actions of higherrank abelian groups on zerodimensional groups are mutually disjoint. The proofs exploit differences in the entropy geometry arising from subdynamics and a form of Abramov–Rokhlin formula for halfspace entropies. We discuss some mutual
Network Theory applied to Linguistics – New Advances in Language Classification and Typology
"... Thanks to the people who made this dissertation possible. Especially I would like to thank my husband Vitali Abramov for his appreciation and support making the preparation of the thesis possible. I thank my whole family Ilya, Ksenia, Maria, mother, father, my dear brother Roman and all my relatives ..."
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Thanks to the people who made this dissertation possible. Especially I would like to thank my husband Vitali Abramov for his appreciation and support making the preparation of the thesis possible. I thank my whole family Ilya, Ksenia, Maria, mother, father, my dear brother Roman and all my