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Durham University

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Staff Profile

Andrew Wade, PhD Durham University

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Professor, Probability in the Department of Mathematical Sciences
Telephone: +44 (0) 191 33 44151
Room number: CM302

Contact Andrew Wade

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.

Research Groups

Department of Mathematical Sciences

  • Probability & Statistics: Probability
  • Probability and Statistics

Research Interests

  • Probability theory
  • Random structures
  • Stochastic processes

Selected 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.

Chapter in book

  • Menshikov, Mikhail V., Mijatović, Aleksandar & Wade, Andrew R. (Accepted). 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.
  • 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

  • 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, Mijatović, Aleksandar & Wade, Andrew R. (2019). Invariance principle for non-homogeneous random walks. Electronic Journal of Probability 24: 48.
  • 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.
  • 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.
  • Cruise, James R. & Wade, Andrew R. (2019). The critical greedy server on the integers is recurrent. Annals of Applied Probability 29(2): 1233-1261.
  • 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.
  • McRedmond, James & Wade, Andrew R. (2018). The convex hull of a planar random walk: perimeter, diameter, and shape. Electronic Journal of Probability 23: 131.
  • 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.
  • 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.
  • 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.
  • Georgiou, Nicholas & Wade, Andrew R. (2014). Non-homogeneous random walks on a semi-infinite strip. Stochastic Processes and their Applications 124(10): 3179-3205.
  • 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.
  • 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.
  • 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.
  • 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. (2012). Rank-driven Markov processes. Journal of Statistical Physics 146(2): 378-407.
  • Grinfeld, Michael, Knight, Philip A. & Wade, Andrew R. (2011). Bak-Sneppen-type models and rank-driven processes. Physical Review E 84(4): 041124.
  • 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.
  • Crane, Edward, Georgiou, Nicholas, Volkov, Stanislav, Wade, Andrew R. & Waters, Robert J. (2011). The simple harmonic urn. Annals of Probability 39(6): 2119-2177.
  • 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.
  • 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., 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.
  • Wade, Andrew R. (2009). Asymptotic theory for the multidimensional random on-line nearest-neighbour graph. Stochastic Processes and their Applications 119(6): 1889-1911.

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