Staff profile

Current funded research programme

Anomalous diffusion via self-interaction and reflection, funded by the EPSRC, runs 2022-2026. This is a joint project between Durham (EP/W00657X/1, £448,461) and Warwick (EP/W006227/1, £457,337).

Research Summary

My research is in probability theory and its applications. My interests include random spatial models and stochastic processes inspired by physics or other applications. Some of my recent work has been on random walks, random spatial graphs, processes in random media, and interacting particle systems. For some more details about some of my research and publications, see here.

• probability theory
• stochastic processes
• random structures

• Probability

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.

Book review

• Wade, Andrew R. (2020). Markov Chains. Newsletter of the European Mathematical Society

Chapter in book

• López Hernández, Alejandro & Wade, Andrew R. (2021). Angular asymptotics for random walks. In A Lifetime of Excursions Through Random Walks and Lévy Processes. Chaumont, Loïc & Kyprianou, Andreas E. Springer. 78: 315-342.
• Menshikov, Mikhail V., Mijatović, Aleksandar & Wade, Andrew R. (2021). Reflecting random walks in curvilinear wedges. In In and Out of Equilibrium 3: Celebrating Vladas Sidoarvicius. Vares, M.E., Fernández, R., Fontes, L.R. & Newman, C.M. Springer. 77: 637-675.
• Cruise, R. James Hryniv, Ostap & Wade, Andrew R. (2014). Random processes. In Mathematical Tools for Physicists. Grinfeld, M. Wiley. pp. 3-38.
• Penrose, Mathew D. & Wade, Andrew R. (2009). Random directed and on-line networks. In New Perspectives in Stochastic Geometry. Kendall, W. S. & Molchanov, I. Oxford University Press. 248-274.

Journal Article

• Malyshev, Vadim, Menshikov, Mikhail V., Popov, Serguei & Wade, Andrew R. (Submitted). Dynamics of finite inhomogeneous particle systems with exclusion interaction.
• Wade, Andrew R. & Grinfeld, Michael (Submitted). Energy-constrained random walk with boundary replenishment.
• da Costa, Conrado Menshikov, Mikhail V. & Wade, Andrew R. (Submitted). Passage-times for partially-homogeneous reflected random walks on the quadrant.
• da Costa, Conrado, Menshikov, Mikhail V. & Wade, Andrew R. (Accepted). Stochastic billiards with Markovian reflections in generalized parabolic domains. Annals of Applied Probability
• Lo, Chak Hei, Menshikov, Mikhail V. & Wade, Andrew R. (Submitted). Strong transience for one-dimensional Markov chains with asymptotically zero drifts.
• Cygan, Wojciech, Sandrić, Nikola, Šebek, Stjepan & Wade, Andrew R. (Submitted). Iterated-logarithm laws for convex hulls of random walks with drift.
• Brešar, Miha, Mijatović, Aleksandar & Wade, Andrew (Submitted). Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability.
• Georgiou, Nicholas & Wade, Andrew R. (2022). Deposition, diffusion, and nucleation on an interval. Annals of Applied Probability 32(6): 4849-4892.
• Lo, Chak Hei, Menshikov, Mikhail V. & Wade, Andrew R. (2022). Cutpoints of non-homogeneous random walks. ALEA - Latin American Journal of Probability and Mathematical Statistics 19: 493-510.
• Menshikov, Mikhail V., Mijatović, Aleksandar & Wade, Andrew R. (2022). Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity. Annales de l'Institut Henri Poincaré
• Comets, Francis, Menshikov, Mikhail V. & Wade, Andrew R. (2020). Random walks avoiding their convex hull with a finite memory. Indagationes Mathematicae 31(1): 117-146.
• 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.
• Georgiou, Nicholas, Mijatović, Aleksandar & Wade, Andrew R. (2019). Invariance principle for non-homogeneous random walks. Electronic Journal of Probability 24: 48.
• Cruise, James R. & Wade, Andrew R. (2019). The critical greedy server on the integers is recurrent. Annals of Applied Probability 29(2): 1233-1261.
• Lo, Chak Hei & Wade, Andrew R. (2019). On the centre of mass of a random walk. Stochastic Processes and their Applications 129(11): 4663-4686.
• McRedmond, James & Wade, Andrew R. (2018). The convex hull of a planar random walk: perimeter, diameter, and shape. Electronic Journal of Probability 23: 131.
• Georgiou, Nicholas, Mijatović, Aleksandar & Wade, Andrew R. (2018). A radial invariance principle for non-homogeneous random walks. Electronic Communications in Probability 23: 56.
• 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.
• Lo, Chak Hei & Wade, Andrew R. (2017). Non-homogeneous random walks on a half strip with generalized Lamperti drifts. Markov Processes and Related Fields 23(1): 125-146.
• 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.
• Wade, Andrew R. & Xu, Chang (2015). Convex hulls of random walks and their scaling limits. Stochastic Processes and their Applications 125(11): 4300-4320.
• Jordan, Jonathan & Wade, Andrew R. (2015). Phase transitions for random geometric preferential attachment graphs. Advances in Applied Probability 47(2): 565-588.
• Grinfeld, Michael, Volkov, Stanislav & Wade, Andrew R. (2015). Convergence in a multidimensional randomized Keynesian beauty contest. Advances in Applied Probability 47(1): 57-82.
• Wade, Andrew R. & Xu, Chang (2015). Convex hulls of planar random walks with drift. Proceedings of the American Mathematical Society 143(1): 433-445.
• Darling, Richard W. R., Penrose, Mathew D., Wade, Andrew R. & Zabell, Sandy L. (2014). Rank deficiency in sparse random GF[2] matrices. Electronic Journal of Probability 19: 83.
• Georgiou, Nicholas & Wade, Andrew R. (2014). Non-homogeneous random walks on a semi-infinite strip. Stochastic Processes and their Applications 124(10): 3179-3205.
• 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). Excursions and path functionals for stochastic processes with asymptotically zero drifts. Stochastic Processes and their Applications 123(6): 1891-1921.
• 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.
• Grinfeld, Michael, Knight, Philip A. & Wade, Andrew R. (2012). Rank-driven Markov processes. Journal of Statistical Physics 146(2): 378-407.
• 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.
• Grinfeld, Michael, Knight, Philip A. & Wade, Andrew R. (2011). Bak-Sneppen-type models and rank-driven processes. Physical Review E 84(4): 041124.
• Crane, Edward, Georgiou, Nicholas, Volkov, Stanislav, Wade, Andrew R. & Waters, Robert J. (2011). The simple harmonic urn. Annals of Probability 39(6): 2119-2177.
• 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., Volkov, Stanislav & Wade, Andrew R. (2010). Passage-time moments and hybrid zones for the exclusion-voter model. Bernoulli 16(4): 1312-1342.
• 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.
• Penrose, Mathew D. & Wade, Andrew R. (2010). Limit theorems for random spatial drainage networks. Advances in Applied Probability 42(3): 659-688.
• 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.
• Wade, Andrew R. (2009). Asymptotic theory for the multidimensional random on-line nearest-neighbour graph. Stochastic Processes and their Applications 119(6): 1889-1911.
• Penrose, Mathew D. & Wade, Andrew R. (2008). Limit theory for the random on-line nearest-neighbor graph. Random Structures and Algorithms 32(2): 125-156.
• 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.
• Penrose, Mathew D. & Wade, Andrew R. (2008). Multivariate normal approximation in geometric probability. Journal of Statistical Theory and Practice 2(2): 293-326.
• 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.
• Wade, Andrew R. (2007). Explicit laws of large numbers for random nearest-neighbour-type graphs. Advances in Applied Probability 39(2): 326-342.
• Penrose, Mathew D. & Wade, Andrew R. (2006). On the total length of the random minimal directed spanning tree. Advances in Applied Probability 38(2): 336-372.
• 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.
• Penrose, Mathew D. & Wade, Andrew R. (2004). Random minimal directed spanning trees and Dickman-type distributions. Advances in Applied Probability 36(3): 691-714.