# 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.