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Durham University

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Staff Profile

Mikhail Menshikov, PhD Moscow State University

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Professor, Probability in the Department of Mathematical Sciences

Contact Mikhail Menshikov (email at mikhail.menshikov@durham.ac.uk)

Research Summary

My research is in stochastic processes, with emphasis on the Lyapunov function method, including random walks, processes in random media, and interacting particle systems. Other interests include percolation theory.

Research Groups

Department of Mathematical Sciences

  • Probability & Statistics: Probability
  • Probability and Statistics

Research Interests

  • Markov chains
  • Probability

Publications

Authored book

  • Menshikov, Mikhail, Popov, Serguei & Wade, Andrew (2016). Non-Homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems. Cambridge: Cambridge University Press.

Journal Article

  • Menshikov, Mikhail & Shcherbakov, Vadim (2020). Localisation in a growth model with interaction. Arbitrary graphs. Latin American Journal of Probability and Mathematical Statistics 17(1): 473-489.
  • Georgiou, Nicholas, Menshikov, Mikhail V., Petritis, Dimitri & Wade, Andrew R. (2019). Markov chains with heavy-tailed increments and asymptotically zero drift. Electronic Journal of Probability 24: 62.
  • Menshikov, Mikhail V., Petritis, Dimitri & Wade, Andrew R. (2018). Heavy-tailed random walks on complexes of half-lines. Journal of Theoretical Probability 31(3): 1819-1859.
  • Costa, Marcelo, Menshikov, Mikhail, Shcherbakov, Vadim & Vachkovskaia, Marina (2018). Localisation in a growth model with interaction. Journal of Statistical Physics 171(6): 1150-1175.
  • Menshikov, Mikhail & Shcherbakov, Vadim (2018). Long term behaviour of two interacting birth-and-death processes. Markov Processes and Related Fields 24(1): 85-106.
  • Georgiou, Nicholas, Menshikov, Mikhail V., Mijatovic, Aleksandar & Wade, Andrew R. (2016). Anomalous recurrence properties of many-dimensional zero-drift random walks. Advances in Applied Probability 48(Issue A): 99-118.
  • Belitsky, V., Menshikov, M.V., Petritis, D. & Vachkovskaia, M. (2016). Random dynamical systems with systematic drift competing with heavy-tailed randomness. Markov Processes And Related Fields 22(4): 629-652.
  • Menshikov, M.V. & Petritis, D. (2014). Explosion, implosion, and moments of passage times for continuous-time Markov chains: A semimartingale approach. Stochastic Processes and their Applications 124(7): 2388-2414.
  • Menshikov, M.V. & Popov, S.Yu. (2014). On range and local time of many-dimensional submartingales. Journal of Theoretical Probability 27(2): 601-617.
  • Hryniv, Ostap, Menshikov, Mikhail V. & Wade, Andrew R. (2013). Excursions and path functionals for stochastic processes with asymptotically zero drifts. Stochastic Processes and their Applications 123(6): 1891-1921.
  • Menshikov, M.V., Sisko, V.V. & Vachkovskaia, M. (2013). Introduction to shape stability for a storage model. Methodology and Computing in Applied Probability 15(1): 125-146.
  • MacPhee, I.M., Menshikov, M.V. & Wade, A.R. (2013). Moments of exit times from wedges for non-homogeneous random walks with asymptotically zero drifts. Journal of Theoretical Probability 26(1): 1-30.
  • Hryniv, Ostap, Menshikov, Mikhail V. & Wade, Andrew R. (2013). Random walk in mixed random environment without uniform ellipticity. Proceedings of the Steklov Institute of Mathematics 282(1): 106-123.
  • MacPhee, I.M., Menshikov, M.V. & Vachkovskaia, M. (2012). Dynamics of the non-homogeneous supermarket model. Stochastic Models 28(4): 533-556.
  • Hryniv, Ostap, MacPhee, Iain M. , Menshikov, Mikhail V. & Wade, Andrew R. (2012). Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips. Electronic Journal of Probability 17: 59, 1-28.
  • Menshikov, Mikhail, Popov, Serguei, Ramírez, Alejandro F. & Vachkovskaia, Marina (2012). On a general many-dimensional excited random walk. Annals of Probability 40(5): 2106-2130.
  • Comets, Francis, Menshikov, Mikhail V., Volkov, Stanislav & Wade, Andrew R. (2011). Random walk with barycentric self-interaction. Journal of Statistical Physics 143(5): 855-888.
  • MacPhee, Iain M., Menshikov, Mikhail V. & Wade, Andrew R. (2010). Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift. Markov Processes and Related Fields 16(2): 351-388.
  • Menshikov, M. V. & Wade, Andrew R. (2010). Rate of escape and central limit theorem for the supercritical Lamperti problem. Stochastic Processes and their Applications 120(10): 2078-2099.
  • Menshikov, M. V., Vachkovskaia, M. & Wade, A. R. (2008). Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains. Journal of Statistical Physics 132(6): 1097-1133.
  • Menshikov, M. V. & Wade, Andrew R. (2008). Logarithmic speeds for one-dimensional perturbed random walks in random environments. Stochastic Processes and their Applications 118(3): 389-416.
  • MacPhee, I. M., Menshikov, M. V., Petritis, D & Popov, S (2008). Polling systems with parameter regeneration, the general case. Annals of Applied Probability 18(6): 2131–2155.
  • Menshikov, Mikhail & Volkov, Stanislav (2008). Urn-related random walk with drift $\rho x^\alpha/t^\beta$. Electronic Journal of Probability 13: 944-960.
  • MacPhee, I.M. , Menshikov, M.V. , Popov, S. & Volkov, S. (2006). Periodicity in the transient regime of exhaustive polling systems. Annals of Applied Probability 16(4): 1816-1850.
  • Andjel, A., Menshikov, M. V. & Sisko, V. (2006). Positive recurrence of processes associated to crystal growth models. Annals of Applied Probability 16(3): 1059-1085.
  • Menshikov, M. V. & Wade, A. R. (2006). Random walk in random environment with asymptotically zero perturbation. Journal of the European Mathematical Society 8(3): 491–513.
  • Menshikov, M.V., Popov, S.Yu., Sisko, V. & Vachkovskaia, M. (2004). On a many-dimensional random walk in a rarefied random environment. 'Markov Process Related Fields 10: 137-160.
  • MacPhee, I.M. & Menshikov, M.V. (2003). Critical random walks on two-dimensional complexes with applications to polling systems. Annals of Applied Probability 13(4): 1399-1422.
  • Menshikov, M.V. & Petritis, D. (2002). Random walks in random environment on trees and multiplicative chaos.
  • Menshikov, M.V., Rybnikov, K.A. & Volkov, S.E. (2002). The loss of tension in an infinite membrane with holes distributed according to a Poisson law. Advances in Applied Probability 34(2): 292-312.
  • Belitsky, V., Ferrari, P., Menshikov, M.V. & Popov, S. Yu. (2001). A mixture of the exclusion process and the voter model. Bernoulli 7(1): 119-144.
  • Menshikov M.V., Popov S. Yu. & Vachkovskaia M. (2001). On the connectivity properties of the complementary set in fractal percolation models. Probability Theory and Related Fields 119(2): 176-186.
  • Menshikov M.V. & Zuyev S. (2001). Polling systems in the critical regime. Stochastic Process Appl 92: 2001-2018.
  • Menshikov, M.V. & Zuyev, S. (2001). Polling systems in the critical rejime. Stochastic Processes and their Applications 92(2): 201-218.
  • Menshikov, M., den Hollander, F. & Popov, S.Yu. (1999). A note on transience versus recurrence for a Branching random walk in random environment. Journal of Statistical Physics 95: 587-614.
  • Menshikov, M., Comets, F. & Popov, S.Yu. (1998). Lyapunov functions for random walks and strings in random environment. Annals of Probability 26: 1433-1445.
  • Menshikov, M., Aspandiiarov, S. & Iasnogorodski, R. (1996). Passage-time moments for non-negative stochastic processes and an application to reflected random walks in a quadrant. Annals of Probability 24: 932-960.
  • Menshikov, M., Grimmett, G.R. & Volkov, S.E. (1996). Random walks in random labyrinths. Markov Processes and Related Fields 2: 69-86.