Urn-related random walk with drift $\rho x^\alpha/t^\beta$
(2008)
Journal Article
Menshikov, M., & Volkov, S. (2008). Urn-related random walk with drift $\rho x^\alpha/t^\beta$. Electronic Journal of Probability, 13, 944-960. https://doi.org/10.1214/ejp.v13-508
Outputs (48)
Logarithmic speeds for one-dimensional perturbed random walks in random environments (2008)
Journal Article
Menshikov, M., & Wade, A. R. (2008). Logarithmic speeds for one-dimensional perturbed random walks in random environments. Stochastic Processes and their Applications, 118(3), 389-416. https://doi.org/10.1016/j.spa.2007.04.011We study the random walk in a random environment on Z+={0,1,2,…}, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) a random walk in a random environment perturbed from Sinai’s r... Read More about Logarithmic speeds for one-dimensional perturbed random walks in random environments.
Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains (2008)
Journal Article
Menshikov, M., Vachkovskaia, M., & Wade, A. (2008). Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains. Journal of Statistical Physics, 132(6), 1097-1133. https://doi.org/10.1007/s10955-008-9578-zWe study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process originates wit... Read More about Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains.
Periodicity in the transient regime of exhaustive polling systems (2006)
Journal Article
MacPhee, I., Menshikov, M., Popov, S., & Volkov, S. (2006). Periodicity in the transient regime of exhaustive polling systems. Annals of Applied Probability, 16(4), 1816-1850. https://doi.org/10.1214/105051606000000376We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the sequence of nodes... Read More about Periodicity in the transient regime of exhaustive polling systems.
Positive recurrence of processes associated to crystal growth models (2006)
Journal Article
Andjel, A., Menshikov, M., & Sisko, V. (2006). Positive recurrence of processes associated to crystal growth models. Annals of Applied Probability, 16(3), 1059-1085. https://doi.org/10.1214/105051606000000079We show that certain Markov jump processes associated to crystal growth models are positive recurrent when the parameters satisfy a rather natural condition.
Random walk in random environment with asymptotically zero perturbation (2006)
Journal Article
Menshikov, M., & Wade, A. (2006). Random walk in random environment with asymptotically zero perturbation. Journal of the European Mathematical Society, 8(3), 491-513. https://doi.org/10.4171/jems/64We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on $\Z^+=\{0,1,2,\ldots\}$, with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results comp... Read More about Random walk in random environment with asymptotically zero perturbation.
On a many-dimensional random walk in a rarefied random environment. (2004)
Journal Article
Menshikov, M., Popov, S., Sisko, V., & Vachkovskaia, M. (2004). On a many-dimensional random walk in a rarefied random environment
Critical random walks on two-dimensional complexes with applications to polling systems (2003)
Journal Article
MacPhee, I., & Menshikov, M. (2003). Critical random walks on two-dimensional complexes with applications to polling systems. Annals of Applied Probability, 13(4), 1399-1422. https://doi.org/10.1214/aoap/1069786503We consider a time-homogeneous random walk Xi = {xi (t)} on a two-dimensional complex. All of our results here are formulated in a constructive way. By this we mean that for any given random walk we can, with an expression using only the first and se... Read More about Critical random walks on two-dimensional complexes with applications to polling systems.
On Random Walks in Random Environment on Trees and Their Relationship with Multiplicative Chaos (2002)
Presentation / Conference Contribution
Menshikov, M., & Petritis, D. (2002, September). On Random Walks in Random Environment on Trees and Their Relationship with Multiplicative Chaos. Presented at International Colloquium of Mathematics and Computer Science, University of Versailles-St-Quentin
The loss of tension in an infinite membrane with holes distributed according to a Poisson law (2002)
Journal Article
Menshikov, M., Rybnikov, K., & Volkov, S. (2002). The loss of tension in an infinite membrane with holes distributed according to a Poisson law. Advances in Applied Probability, 34(2), https://doi.org/10.1239/aap/1025131219What is the effect of punching holes at random in an infinite tensed membrane? When will the membrane still support tension? This problem was introduced by Connelly in connection with applications of rigidity theory to natural sciences. The answer cl... Read More about The loss of tension in an infinite membrane with holes distributed according to a Poisson law.