# Staff Profile

## Mikhail Menshikov, PhD Moscow State University

**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.