Andrew Wade - Research

Gallery

Here are some pictures linking to a few themes from my work

Non-homogeneous random walks
With Nicholas Georgiou, Ostap Hryniv, Chak Hei Lo, Iain MacPhee, Mikhail Menshikov, Aleksandar Mijatović, and Serguei Popov

Stochastic processes with reflections

Stochastic processes with reflections
With Miha Brešar, Conrado da Costa, Michael Grinfeld, Vadim Malyshev, Mikhail Menshikov, Aleksandar Mijatović, Serguei Popov, and Marina Vachkovskaia

Self-interacting random walks

Self-interacting random walks
With Francis Comets, Mikhail Menshikov, and Stas Volkov

Convex hull of random walk

Convex hulls of random walks
With Wojciech Cygan, James McRedmond, Nikola Sandrić, Stjepan Šebek, Chang Xu

Random spatial graphs

Random spatial graphs
With Nicholas Georgiou, Jonathan Jordan, Mathew Penrose, and Qasem Tawhari

Rank-driven process

Rank-driven processes
With Michael Grinfeld, Philip Knight, and Stas Volkov

Collaborators

Alejandro López Hernández

James McRedmond

Robert Waters

Chang Xu

Sandy Zabell

PhD students

Qasem Tawhari (2019–2024). Jointly supervised with Nicholas Georgiou. Thesis: "Random directional nearest-neighbour graphs".

Clare Wallace (2017–2021). Jointly supervised with Ostap Hryniv. Thesis: "Conditional limit theorems for renewal random walks".

James McRedmond (2015–2019). Jointly supervised with Ostap Hryniv. Thesis: "Convex hulls of random walks".

Marcelo Costa (2014–2018). Jointly supervised with Mikhail Menshikov. Thesis: "Cooperative models of stochastic growth".

Chak Hei Lo (2014–2018). Jointly supervised with Mikhail Menshikov. Thesis: "On some random walk problems".

Chang Xu (2011–2017). Jointly supervised with Xuerong Mao. Thesis: "Convex hulls of planar random walks".

Publications

There is a list of most of my published work at MathSciNet or Zentralblatt. Preprint versions of most of my papers are available for download from arXiv.

Pre-publication versions of some of my papers are available via Durham Research Online.

You can also look at my researcher profiles at google scholar, Web of Science, ResearchGate, or ORCiD.

Preprints/submitted work

Superdiffusive limits for Bessel-driven stochastic kinetics with Miha Brešar, Conrado da Costa, and Aleksandar Mijatović. Submitted. Abstract. ArXiv.

Superdiffusive planar random walks with polynomial space-time drifts with Conrado da Costa, Mikhail Menshikov, and Vadim Shcherbakov. Submitted. Abstract. ArXiv.

Iterated-logarithm laws for convex hulls of random walks with drift with Wojciech Cygan, Nikola Sandrić, and Stjepan Šebek. Submitted. Abstract. ArXiv.

Passage-times for partially-homogeneous reflected random walks on the quadrant with Conrado da Costa and Mikhail Menshikov. Submitted. Abstract. ArXiv.

Book

Non-homogeneous Random Walks with Mikhail Menshikov and Serguei Popov. Cambridge University Press, December 2016. Errata.

Refereed journal articles

Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability with Miha Brešar and Aleksandar Mijatović. To appear in Annals of Probability. Abstract. ArXiv.

Strong transience for one-dimensional Markov chains with asymptotically zero drifts with Chak Hei Lo and Mikhail V. Menshikov. Stochastic Processes and their Applications 170 (2024) article no. 104260. Abstract. Article. ArXiv.

Stochastic billiards with Markovian reflections in generalized parabolic domains with Conrado da Costa and Mikhail Menshikov. Annals of Applied Probability 33 (2023) 5459–5496. Abstract. Article. ArXiv.

Dynamics of finite inhomogeneous particle systems with exclusion interaction with Vadim Malyshev, Mikhail Menshikov, and Serguei Popov. Journal of Statistical Physics 190 (2023) article no. 184. Abstract. Article. ArXiv.

Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity with Mikhail Menshikov and Aleksandar Mijatović. Annales de l'Institut Henri Poincaré 59 (2023) 1813–1843. Abstract. Article. ArXiv.

Energy-constrained random walk with boundary replenishment with Michael Grinfeld. Journal of Statistical Physics 190 (2023) article no. 155. Abstract. Article. ArXiv.

Deposition, diffusion, and nucleation on an interval with Nicholas Georgiou. Annals of Applied Probability 32 (2022) 4849–4892. Abstract. Article. ArXiv.

Cutpoints of non-homogeneous random walks with Chak Hei Lo and Mikhail Menshikov. Latin American Journal of Probability and Mathematical Statistics 19 (2022) 493–510. Abstract. Article. ArXiv.

Random walks avoiding their convex hull with a finite memory with Francis Comets and Mikhail Menshikov. Indagationes Mathematicae 31 (2020) 117–146. Abstract. Article. ArXiv.

On the centre of mass of a random walk with Chak Hei Lo. Stochastic Processes and their Applications 129 (2019) 4663–4686. Abstract. Article. ArXiv.

Markov chains with heavy-tailed increments and asymptotically zero drift with Nicholas Georgiou, Mikhail Menshikov, and Dimitri Petritis. Electronic Journal of Probability 24 (2019) paper no. 62. Abstract. Article. ArXiv.

Invariance principle for non-homogeneous random walks with Nicholas Georgiou and Aleksandar Mijatović. Electronic Journal of Probability 24 (2019) paper no. 48. Abstract. Article. ArXiv.

The critical greedy server on the integers is recurrent with James Cruise. Annals of Applied Probability 29 (2019) 1233–1261. Abstract. Article. ArXiv.

The convex hull of a planar random walk: perimeter, diameter, and shape with James McRedmond. Electronic Journal of Probability 23 (2018) paper no. 131. Abstract. Article. ArXiv.

A radial invariance principle for non-homogeneous random walks with Nicholas Georgiou and Aleksandar Mijatović. Electronic Communications in Probability 23 (2018) paper no. 56. Abstract. Article. ArXiv.

Heavy-tailed random walks on complexes of half-lines with Mikhail Menshikov and Dimitri Petritis. Journal of Theoretical Probability 31 (2018) 1819–1859. Abstract. Article. ArXiv.

Non-homogeneous random walks on a half strip with generalized Lamperti drifts with Chak Hei Lo. Markov Processes and Related Fields23 (2017) 125–146. Abstract. ArXiv.

Anomalous recurrence properties of many-dimensional zero-drift random walks with Nicholas Georgiou, Mikhail Menshikov and Aleksandar Mijatović. Advances in Applied Probability 48A (2016) 99–118. Abstract. Article. ArXiv .

Convex hulls of random walks and their scaling limits with Chang Xu. Stochastic Processes and their Applications 125 (2015) 4300–4320. Abstract. Article. ArXiv .

Phase transitions for random geometric preferential attachment graphs with Jonathan Jordan. Advances in Applied Probability 47 (2015) 565–588. Abstract. Article. ArXiv .

Convergence in a multidimensional randomized Keynesian beauty contest with Michael Grinfeld and Stanislav Volkov. Advances in Applied Probability 47 (2015) 57–82. Abstract. Article. ArXiv.

Convex hulls of planar random walks with drift with Chang Xu. Proceedings of the American Mathematical Society 143 (2015) 433–445. Abstract. Article. ArXiv.

Rank deficiency in sparse random GF[2] matrices with Richard Darling, Mathew Penrose and Sandy Zabell. Electronic Journal of Probability 19 (2014) paper no. 83. Abstract. Article. ArXiv .

Non-homogeneous random walks on a semi-infinite strip with Nicholas Georgiou. Stochastic Processes and their Applications 124 (2014) 3179–3205. Abstract. Article. ArXiv.

Random walk in mixed random environment without uniform ellipticity with Ostap Hryniv and Mikhail Menshikov. Proceedings of the Steklov Institute of Mathematics 282 (2013) 106–123. Abstract. Article. ArXiv.

Excursions and path functionals for stochastic processes with asymptotically zero drifts with Ostap Hryniv and Mikhail Menshikov. Stochastic Processes and their Applications 123 (2013) 1891–1921. Abstract. Article. ArXiv.

Moments of exit times from wedges for non-homogeneous random walks with asymptotically zero drifts with Iain MacPhee and Mikhail Menshikov. Journal of Theoretical Probability 26 (2013) 1–30. Abstract. Article. ArXiv.

Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips with Ostap Hryniv, Iain MacPhee and Mikhail Menshikov. Electronic Journal of Probability 17 (2012) paper no. 59. Abstract. Article. ArXiv.

Rank-driven Markov processes with Michael Grinfeld and Philip Knight. Journal of Statistical Physics 146 (2012) 378–407. Abstract. Article. ArXiv.

The simple harmonic urn with Edward Crane, Nicholas Georgiou, Stanislav Volkov and Robert Waters. Annals of Probability 39 (2011) 2119–2177. Abstract. Article. ArXiv.

Bak–Sneppen-type models and rank-driven processes with Michael Grinfeld and Philip Knight. Physical Review E 84 (2011) 041124. Abstract. Article. ArXiv.

Random walk with barycentric self-interaction with Francis Comets, Mikhail Menshikov and Stanislav Volkov. Journal of Statistical Physics 143 (2011) 855–888. Abstract. Article. ArXiv.

Passage-time moments and hybrid zones for the exclusion-voter model with Iain MacPhee, Mikhail Menshikov and Stanislav Volkov. Bernoulli 16 (2010) 1312–1342. Abstract. Article. ArXiv.

Limit theorems for random spatial drainage networks with Mathew Penrose. Advances in Applied Probability 42 (2010) 659–688. Abstract. Article. ArXiv.

Rate of escape and central limit theorem for the supercritical Lamperti problem with Mikhail Menshikov. Stochastic Processes and their Applications 120 (2010) 2078–2099. Abstract. Article. ArXiv.

Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift with Iain MacPhee and Mikhail Menshikov. Markov Processes and Related Fields 16 (2010) 351–388. Abstract. Article. ArXiv.

Asymptotic theory for the multidimensional random on-line nearest-neighbour graph. Stochastic Processes and their Applications 119 (2009) 1889–1911. Abstract. Article. ArXiv.

Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains with Mikhail Menshikov and Marina Vachkovskaia. Journal of Statistical Physics 132 (2008) 1097–1133. Abstract. Article. ArXiv.

Multivariate normal approximation in geometric probability with Mathew Penrose. Journal of Statistical Theory and Practice 2 (2008) 293–326. Abstract. Article. ArXiv.

Logarithmic speeds for one-dimensional perturbed random walk in random environment with Mikhail Menshikov. Stochastic Processes and their Applications 118 (2008) 389–416. Abstract. Article. ArXiv.

Limit theory for the random on-line nearest-neighbor graph with Mathew Penrose. Random Structures and Algorithms 32 (2008) 125–156. Abstract. Article. ArXiv.

Explicit laws of large numbers for random nearest-neighbour-type graphs. Advances in Applied Probability 39 (2007) 326–342. Abstract. Article. ArXiv.

Random walk in random environment with asymptotically zero perturbation with Mikhail Menshikov. Journal of the European Mathematical Society 8 (2006) 491–513. Abstract. Article. ArXiv.

On the total length of the random minimal directed spanning tree with Mathew Penrose. Advances in Applied Probability 38 (2006) 336–372. Abstract. Article. Extended ArXiv version.

Random minimal directed spanning trees and Dickman-type distributions with Mathew Penrose. Advances in Applied Probability 36 (2004) 691–714. Abstract. Article. Preprint.

Contributions to edited books

Angular asymptotics for random walks with Alejandro López Hernández. pp. 315–342 in A Lifetime of Excursions Through Random Walks and Lévy Processes: A Volume in Honour of Ron Doney’s 80th Birthday, Eds. L. Chaumont and A.E. Kyprianou. Progress in Probability 78, Springer, December 2021. Abstract. ArXiv.

Reflecting random walks in curvilinear wedges with Mikhail Menshikov and Aleksandar Mijatović. Chapter 26, pp. 637–675 in In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, Eds. M.E. Vares, R. Fernández, L.R. Fontes, C.M. Newman, Progress in Probability 77, Springer, February 2021. Abstract. ArXiv.

Stochastic processes with James Cruise and Ostap Hryniv. Chapter 1, pp. 3–38 in Mathematical Tools for Physicists, 2nd ed., Ed. M. Grinfeld, Wiley, November 2014. Abstract. Available as a chapter of the Encyclopedia of Applied Physics.

Random directed and on-line networks with Mathew Penrose. Section II.7, pp. 248–274 in New Perspectives in Stochastic Geometry, Eds. W.S. Kendall and I. Molchanov, Oxford University Press, November 2009. Abstract.

Other

Book review: Markov chains by Douc, Moulines, Priouret and Soullier (Springer, 2018). Newsletter of the European Mathematical Society, Issue 116 (June 2020), 48–49.