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## Строгая эргодичность коллективного случайного блуждания

Доклады Академии наук. 2013. Т. 448. № 6. С. 629-632.

We give conditions for unique ergodicity for a discrete time collective

random walk on a continuous circle. Individual particles in this collective

motion perform independent (and different) random walks conditioned

by the assumption that the particles cannot overrun each other.

Deterministic version of this system is studied as well.

Blank M., Nonlinearity 2014 Vol. 27 No. 5 P. 953-971

We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that the particles cannot overrun each other. Additionally to sufficient conditions for the unique ergodicity we discover a new and unexpected way ...

Added: November 21, 2014

Afanasyeva L. G., Tkachenko A., Theory of Probability and Its Applications 2014 Vol. 58 No. 2 P. 174-192

We consider the multichannel queueing system with nonidentical servers and regenerative input flow. The necessary and sufficient condition for ergodicity is established, and functional limit theorems for high and ultra-high load are proved. As a corollary, the ergodicity condition for queues with unreliable servers is obtained. Suggested approaches are used to prove the ergodic theorem ...

Added: August 20, 2014

Kleptsyn V., Alvarez S., Malicet D. et al., / Cornell University. Series math "arxiv.org". 2015.

Added: June 22, 2016

Tkachenko A., / Высшая школа экономики. Series WP BRP "Science, Technology and Innovation". 2013. No. 14.

Motivated by the application to telephone call centers this paper is focused on the multichannel queueing system with heterogeneous servers, regenerative input flow and balking. Servers times are random variables but not necessary exponential. If a new customer encountering j other customers in the system then it stays for service with probability fj and gets ...

Added: August 1, 2013

Skripchenko A., Hubert P., Avila A., / Cornell University. Series math "arxiv.org". 2014. No. 1412.7913.

We study chaotic plane sections of some particular family of triply periodic surfaces. The question about possible behavior of such sections was posed by S. P. Novikov. We prove some estimations on diffusion rate of these sections using the connection between Novikov's problem and systems of isometries - some natural generalization of interval exchange transformations. ...

Added: January 27, 2015

Ткаченко А.В., Вестник Московского университета. Серия 1: Математика. Механика 2014 № 1 С. 53-57

This paper is focused on multichannel queueing system with heterogeneous servers and regenerative input flow in a random environment. The environment can destroy all the system and then system is reconstructed. Ergodicity condition of the system is obtained. ...

Added: May 11, 2013

Tkachenko A., Esaulov D., Applied Mathematical Modelling 2016

This paper is focused on a multichannel queueing system with heterogeneous servers, regenerative input flow, and balking. Service times are random variables but not necessary exponential. If a new customer encounters j other customers in the system, then it joins the queue with probability fj and leaves with probability 1-fj . For this system the ...

Added: October 19, 2016

А. В. Ткаченко, Вестник Московского университета. Серия 1: Математика. Механика 2013 № 2 С. 12-17

This paper is devoted to $M|GI|1|\infty$ queueing system with unreliable server and customer service times depending on the system state. Condition of ergodicity and generating function are found in the stationary state. ...

Added: March 27, 2013

Bizyaev I. A., Борисов А. В., Мамаев И. С., Труды Математического института им. В.А. Стеклова РАН 2016 Т. 294 С. 268-292

This paper is concerned with the nonholonomic Suslov problem and its generalization proposed by Chaplygin. The issue of the existence of an invariant measure with singular density (having singularities at some points of phase space) is discussed. ...

Added: April 4, 2017

Tkachenko A., Moscow University Mathematics Bulletin 2014 Vol. 69 No. 1 P. 37-40

This paper is focused on a multichannel queueing system with heterogeneous servers and regenerative input flow operating in a random environment. The environment can destroy the whole system and the system is reconstructed after that. The necessary and sufficient ergodicity condition is obtained for the system. ...

Added: August 20, 2014

Veretennikov A., Veretennikova M., / Cornell University. Series "Working papers by Cornell University". 2019.

New convergence rate asymptotic bound for a class of homogeneous Markov chains is established. ...

Added: November 14, 2019

Blank M., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2015 Т. 461 № 2 С. 1-5

We study the functional properties of the concept of interlacing introduced by I.M. Gelfand and show that in the context of collective random walks, this property leads to synchronization. ...

Added: March 20, 2015

Blank M., Nonlinearity 2012 Vol. 25 No. 12 P. 3389-3408

We study ergodic properties of a family of traffic maps acting in
the space of bi-infinite sequences of real numbers. The corresponding
dynamics mimics the motion of vehicles in a simple traffic flow, which
explains the name. Using connections to topological Markov chains we obtain
nontrivial invariant measures, prove their stochastic stability, and
calculate the topological entropy. Technically these results ...

Added: November 26, 2014

Blank M., Russian Mathematical Surveys 2016 Vol. 71 No. 3 P. 588-590

We present sufficient (and in some cases necessary) conditions under
which the time average along a trajectory of a measurable dynamical
system coincides with the space average for almost all initial points
with respect to a given reference measure (rather than to an ergodic one,
which may not exist in general). ...

Added: November 13, 2016

Tumanov M., Абдуллин С., Вестник Московского государственного университета леса - Лесной вестник 2015 № 3 С. 173-177

Discusses frequency methods to ensure the accuracy of the control system with model lag and the connection with ergodic theory (the theory of quasi-periodic functions) in the case where the delay model differs from the true. ...

Added: August 27, 2015

Боровков А. А., Cambridge University Press, 2020

This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established ...

Added: March 30, 2021

Veretennikov A., Veretennikova M., Doklady Mathematics 2020 Vol. 101 No. 1 P. 12-15

Изучаются улучшенные оценки скорости сходимости для эргодических однородных цепей Маркова. Даны примеры сравнения с классическими оценками. ...

Added: October 29, 2019

Афанасьева Л. Г., Ткаченко А.В., Теория вероятностей и ее применения 2013 Т. 58 № 2 С. 210-234

We consider a multichannel queuing system with heterogeneous servers and regenerative input flow. The necessary and sufficient condition is established and functional limit theorems are proved in overloaded and critically loaded regimes. The ergodicity condition is obtained for multichannel system with unreliable servers. Some approaches for ergodicity of systems with abandonment are discussed. ...

Added: March 31, 2013

Bogachev V., Veretennikov A., Shaposhnikov S., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2015 Т. 460 № 5 С. 507-511

Методами уравнений в частных производных установлены достаточные условия дифференцируемости инвариантных мер диффузионных процессов по параметру ...

Added: October 11, 2015

Dynnikov I., Hubert P., Skripchenko A., International Mathematics Research Notices 2023 Vol. 2023 No. 8 P. 6461-6503

At the beginning of the 80s, H. Masur and W. Veech started the study of generic properties of interval exchange transformations (IETs) proving that almost every such transformation is uniquely ergodic. About the same time, S. Novikov’s school and French mathematicians independently discovered very intriguing phenomena for classes of measured foliations on surfaces and respective ...

Added: December 28, 2023

Blank M., Markov Processes and Related Fields 2012 Vol. 18 P. 531-552

We study discrete time totally asymmetric exclusion process
(TASEP) describing collective random walk of countable particle
configurations in heterogeneous continuum. A typical example of this sort is a traffic flow
model with obstacles: traffic lights, speed bumps, spatially varying local
velocities etc. Ergodic properties of such systems are studied, in
particular we obtain the so called Fundamental Diagram: dependence of ...

Added: November 26, 2014

Zaev D., / Cornell University. Series math "arxiv.org". 2015.

We consider L^p-Wasserstein distances on a subset of probability measures. If the subset of interest appears to be a simplex, these distances are determined by their values on extreme points of the simplex. We show that this fact is a corollary of the following decomposition result: an optimal transport plan can be represented as a mixture ...

Added: May 25, 2015

Konakov V., Menozzi S., / Cornell University. Series arXiv "math". 2023. No. 2312.06222.

Abstract. We prove central and local limit theorems for random walks on the Poincar´e hyperbolic space of
dimension n ě 2. To this end we use the ball model and describe the walk therein through the M¨obius addition
and multiplication. This also allows to derive a corresponding law of large numbers. ...

Added: December 12, 2023

Bizyaev I. A., Borisov A., Mamaev I., Regular and Chaotic Dynamics 2016 Vol. 21 No. 1 P. 136-146

This paper is concerned with the motion of the Chaplygin sleigh on the surface of a circular cylinder. In the case of inertial motion, the problem reduces to the study of the dynamical system on a (two-dimensional) torus and to the classification of singular points. Particular cases in which the system admits an invariant measure ...

Added: April 5, 2017