Research

Research in our group covers a diverse range of theoretical and applied probability and stochastic processes, including: stochastic approximation, the theory of queues and stochastic networks, random walks, random graphs and combinatorial structures, reinforcement processes, interacting particle systems, stochastic dynamical systems.

Recent examples include:

M Kieburg, SH Li, J Zhang, and PJ Forrester. Cyclic Pólya Ensembles on the Unitary Matrices and their Spectral Statistics. Constructive Approximation, 1-46 (2023).

A.D. Barbour, G. Brightwell and M. J. Luczak. Long-term concentration of measure and cut-off. Stochastic Processes and their Applications 152, 378-423 (2022).

Beaton, N. and Holmes, M. The mean square displacement of random walk on the Manhattan lattice. Statistics and Probability Letters, Volume 193, (2023), 109706

P. Taylor. Spatial queues with a moving server. Queueing Systems, vol.100,no.3-4,, pp. 261-263, (2022).

D. Bertacchi, P. Braunsteins, S. Hautphenne, and F. Zucca.
Extinction probabilities in branching processes with countably many types: a general framework. ALEA, Lat. Am. J. Probab. Math. Stat., 19:311-338, (2022).

Holmes, M. and Salisbury, T. A shape theorem for the orthant model. Annals of Probability 49:3, 1237-1256, (2021)

D. Beliaev, S. Muirhead and A. Rivera. A covariance formula for topological events of smooth Gaussian fields. Ann. Probab. 48(6) (2020), 2845–2893.

D. Beliaev, M. McAuley and S. Muirhead . On the number of excursion sets of planar Gaussian fields. Probab. Theory Related Fields 178(3–4) (2020), 655–698

Borovkov, K. and He, P. Limit theorems for record indicators in threshold Fα-schemes. To appear in Theory Probab. Appl. (2020) arXiv:1903.03753

Hirsch, C., Holmes, M. , and Kleptsyn, V. Absence of WARM percolation in the very strong reinforcement regime. Ann. Appl. Probab. 31 (1), 199-217, (2021).

YP Förster, M Kieburg and H Kösters. Polynomial ensembles and Pólya frequency functions. J. Theoretical Probability 34 (4), 1917-1950, (2021).

Bostan, A., Elvey-Price, A., Guttmann, A.J., and Maillard, J.-M.  Stieltjes moment sequences for pattern-avoiding permutations Electronic J. of Combinatorics Volume 27, Issue 4 (2020).

de Gier, J., Kenyon, R., and Watson, S.S.  Limit shapes for the asymmetric five vertex model. Communications in Mathematical Physics volume 385, pages 793–836 (2021).

Barbour, A., and Xia, A. Multivariate approximation in total variation using local dependence. Electr. J. Prob. 24 (2019), paper no. 27, 1-35.

Barbour, A. and Rollin, A. Central limit theorems in the configuration model.  Ann. Appl. Probab. 29, 1046-1069, 2019.

Reinert, G. and Ross, N. Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs. Ann. Appl. Probab. 29 (5), 3201-3229 (2019).

Holmes, M. and Perkins, E.  On the range of lattice models in high dimensions.  Prob. Th. Related Fields. (2020).

P. Braunsteins and S. Hautphenne. Extinction probabilities of Lower Hessenberg branching processes with countably many types. Annals of Applied Probability, 2019, 29(5):2782-2818.

Geng, X. and Boedihardjo, H. Tail asymptotics of the Brownian signature.  Trans. Amer. Math. Soc.: 585-614, 2019.

Beaton, N.R., Eng, J.W. and Soteros, C.E.  Knotting statistics for polygons in lattice tubes
Journal of Physics A: Mathematical and Theoretical 52, (2019), 14403.

Borovkov, K. Gaussian process approximations for multicolor Pólya urn models. J. of Applied Probability, 58(1), 274-286. (2020)

Bean, N. G., Latouche G., and  Taylor P. Physical Interpretations for Quasi-Birth-and-Death Process Algorithms. Queueing Models and Service Management. 1(2), 59-78, 2018.

Chen, Z., de Gier, J., Hiki, I.  and Sasamoto, T.  Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process. Phys. Rev. Lett. 120, 2018.