Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains

DOI10.1007/s10955-008-9578-zzbMath1157.82036arXiv0802.1865OpenAlexW3098937740MaRDI QIDQ960155

Marina Vachkovskaia, Andrew R. Wade, Mikhail V. Menshikov

Publication date: 16 December 2008

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1865

zbMATH Keywords

rarefied gas dynamicsKnudsen random walkalmost-sure boundsLamperti problembirth-and-death chainrecurrence/transiencerandom reflectionsstochastic billiards

Mathematics Subject Classification ID

Kinetic theory of gases in time-dependent statistical mechanics (82C40) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

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Cites Work

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• A law of the iterated logarithm for a class of polynomial hypergroups
• Criteria for the recurrence or transience of stochastic process. I
• Random walks
• On Knudsen flows within thin tubes
• Certain limit theorems for an elementary Markov random walk
• Strong laws of large numbers for random walks associated with a class of one-dimensional convolution structures
• The Boltzmann equation and its applications
• Lyapunov functions for random walks and strings in random environment
• A law of the iterated logarithm for Markov chains on \(\mathbb{N}_ 0\) associated with orthogonal polynomials
• Markov processes with asymptotically zero drifts
• Semi-dispersing billiards with an infinite cusp. I
• Stochastic billiards on general tables
• On the behavior of random walk around heavy points
• Logarithmic speeds for one-dimensional perturbed random walks in random environments
• Criteria for stochastic processes. II: Passage-time moments
• Recurrence-time moments in random walks
• Comportement asymptotique des marches aleatoires associees aux polynomes de Gegenbauer et applications
• Probability with Martingales
• An infinite step billiard
• Escape orbits for non-compact flat billiards
• Topics in the Constructive Theory of Countable Markov Chains
• A Local Limit Theorem for a Certain Class of Random Walks
• An extension of Khintchine's estimate for large deviations to a class of markov chains converging to a singular diffusion
• Semidispersing billiards with an infinite cusp. II
• First Passage and Recurrence Distributions
• Billiards in a general domain with random reflections