arXiv subjects

Evgeny Verbitskiy

Publications and source records attributed to Evgeny Verbitskiy.

25 records · Page 2Linked to original sources

arXiv2009

Entropy and growth rate of periodic points of algebraic Z^d-actions

Expansive algebraic Z^d-actions corresponding to ideals are characterized by the property that the complex variety of the ideal is disjoint from the multiplicative unit torus. For such actions it is known that the limit for the growth rate of periodic points exists and equals the entropy of the action. We extend this result to actions for which the complex variety intersects the multiplicative torus in a finite set. The main technical tool is the use of homoclinic points which decay rapidly enough to be summable.

math.DS↗

arXiv2009

Abelian Sandpiles and the Harmonic Model

We present a construction of an entropy-preserving equivariant surjective map from the $d$-dimensional critical sandpile model to a certain closed, shift-invariant subgroup of $\mathbb{T}^{\mathbb{Z}^d}$ (the `harmonic model'). A similar map is constructed for the dissipative abelian sandpile model and is used to prove uniqueness and the Bernoulli property of the measure of maximal entropy for that model.

math.DS↗

arXiv2007

Smooth Rényi Entropy of Ergodic Quantum Information Sources

We prove that the average smooth Renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the Shannon entropy rate for a classical information source and the von Neumann entropy rate for a quantum information source.

quant-ph↗

arXiv2006

Dynamics & Stochastics: Festschrift in honor of M. S. Keane

The present volume is a Festschrift for Mike Keane, on the occasion of his 65th birthday on January 2, 2005. It contains 29 contributions by Mike's closest colleagues and friends, covering a broad range of topics in Dynamics and Stochastics. To celebrate Mike's scientific achievements, a conference entitled ``Dynamical Systems, Probability Theory and Statistical Mechanics'' was organized in Eindhoven, The Netherlands, during the week of January 3--7, 2005. This conference was hosted jointly by EURANDOM and by Philips Research. It drew over 80 participants from 5 continents, which is a sign of the warm affection and high esteem for Mike felt by the international mathematics community.

math.PR↗

arXiv2006

Entropy of a bit-shift channel

We consider a simple transformation (coding) of an iid source called a bit-shift channel. This simple transformation occurs naturally in magnetic or optical data storage. The resulting process is not Markov of any order. We discuss methods of computing the entropy of the transformed process, and study some of its properties.

math.DS↗

arXiv2006

On approximate pattern matching for a class of Gibbs random fields

We prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice $\mathbb{Z}^d$, $d\ge2$. From this result, we deduce a law of large numbers and a large deviation result for the waiting time of distorted patterns.

math.PR↗

arXiv2002

Large Deviations and a Fluctuation Symmetry for Chaotic Homeomorphisms

We consider expansive homeomorphisms with the specification property. We give a new simple proof of a large deviation principle for Gibbs measures corresponding to a regular potential and we establish a general symmetry of the rate function for the large deviations of the antisymmetric part, under time-reversal, of the potential. This generalizes the Gallavotti-Cohen fluctuation theorem to a larger class of chaotic systems.

nlin.CD↗