# Staff Profile

## Andrew Wade, PhD Durham University

**Professor, Probability in the Department of Mathematical Sciences**

Telephone: +44 (0) 191 33 44151

Room number: CM302

### 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.