# Staff profile

Overview

## Andrew Wade

Professor, Probability

PhD Durham University

Affiliation | Room number | Telephone |
---|---|---|

Professor, Probability in the Department of Mathematical Sciences | MCS3022 | +44 (0) 191 33 44151 |

### Biography

##### 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.

### Research interests

- probability theory
- stochastic processes
- random structures

### Research groups

- Probability

### Awarded Grants

- 2019: PiNE: Probability In the North East(£988.09 from The London Mathematical Society)
- 2018: Probability in the North East (PiNE) 2018/19(£1500.00 from The London Mathematical Society)
- 2017: Probability in the North East(£1600.00 from The London Mathematical Society)
- 2016: Probability in the North East(£1200.00 from London Mathematical Society)
- 2015: Probability on the North-East(£1847.24 from London Mathematical Society)
- 2014: Aspects of Random Walks(£598.00 from London Mathematical Society)
- 2013: Non-homogenous random walks(£91911.00 from Epsrc)

### Publications

Authored book

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

- Lo, Chak Hei, Menshikov, Mikhail V. & Wade, Andrew R. (Submitted). Strong transience for one-dimensional Markov chains with asymptotically zero drifts.
- Malyshev, Vadim, Menshikov, Mikhail V., Popov, Serguei & Wade, Andrew R. (Submitted). Dynamics of finite inhomogeneous particle systems with exclusion interaction.
- Brešar, Miha, Mijatović, Aleksandar & Wade, Andrew (Submitted). Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability.
- da Costa, Conrado, Menshikov, Mikhail V. & Wade, Andrew R. (Accepted). Stochastic billiards with Markovian reflections in generalized parabolic domains.
*Annals of Applied Probability* - 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. - 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. - 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. - Grinfeld, Michael, Knight, Philip A. & Wade, Andrew R. (2011). Bak-Sneppen-type models and rank-driven processes.
*Physical Review E***84**(4): 041124. - 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. - 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. - 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. - 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). Limit theory for the random on-line nearest-neighbor graph.
*Random Structures and Algorithms***32**(2): 125-156. - 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. - 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. (2006). On the total length of the random minimal directed spanning tree.
*Advances in Applied Probability***38**(2): 336-372. - Penrose, Mathew D. & Wade, Andrew R. (2004). Random minimal directed spanning trees and Dickman-type distributions.
*Advances in Applied Probability***36**(3): 691-714.

### Supervision students

### Qasem Tawhari

4PROB