Probability is both a fundamental way of viewing the world, and a core area of mathematics. Probability theory is concerned with the analysis of mathematical models of random phenomena, as occur in many branches of science. The group Probability and Applications at QMUL is engaged in numerous research activities, including stochastic processes, statistics, random discrete structures, random matrices and stochastic optimisation, as well as in applications of probability to statistical physics, modelling of epidemics, networks, financial engineering and other areas.

Some recent publications

S. Sodin and I. Goldsheid (2018) Real eigenvalues in the non-Hermitian Anderson model, Ann. Appl. Probab. 28, 3075-3093.

A. Gnedin, A. Iksanov, A. Marynych and M. Moehle (2018) The collision spectrum of Lambda-coalescents, Ann. Appl. Prob. 28, 3857-3883.

M. Shamis and O. Zeitouni (2018), The Curie-Weiss model with complex temperature:

phase transitions, J. Stat. Phys. 172, 569-591.

S. Muirhead, R. Pymar and N. Sidorova (2018) Delocalising the parabolic Anderson model through partial duplication of the potential, Probab. Theory Rel. Fields 171, 917–979*.*

D. Beliaev and S. Muirhead (2018) Discretisation schemes for level sets of planar Gaussian fields, Commun. Math. Phys. 359(3), 869–913.

A. Gnedin and V. Gorin (2015) Record-dependent measures of the symmetric groups, Random Structures and Algorithms 46, 688-706.

P.V. Gapeev and N. Rodosthenous (2014) Optimal stopping problems in diffusion-type models with running maxima and drawdowns, J. Appl. Probab. 51, 799-817.

I. Goldsheid and D. Dolgopyat (2013) Limit theorems for random walks on a strip in subdiffusive regimes, Nonlinearity 26, 1743-1782.

Y. Fyodorov, B.Khoruzhenko and A. Nock (2013) Universal K-matrix distribution in beta=2 ensembles of random matrices, J. Phys. A, Math. Theor. 46, No 26, Article ID 262001.

T. De Angelis, G. Ferrari and J. Moriarty (2017). Nash equilibria of threshold type for two-player nonzero-sum games of stopping. To appear in Annals of Applied Probability.

V.V. Anisimov, W.Y. Yeung, D.S. and D. S. Coad (2017). Imbalance properties of centre-stratified permuted-block and complete randomisation for several treatments in a clinical trial. Statistics in Medicine, 36, 1302-1318.

S. Sodin (2015) A limit theorem at the spectral edge for corners for time-dependent Wigner matrices, Int. Math. Res. Not. IMRN 17, 7575-7607.

Aizenman, M., Peled, R., Schenker, J., Shamis, M. and Sodin, S. Matrix regularizing effects of Gaussian perturbations. Commun. Contemp. Math. 19 (2017), no. 3, 1750028, 22 pp.

N. Rodosthenous and H. Zhang (2017). Beating the Omega Clock: An Optimal Stopping Problem with Random Time-Horizon Under Spectrally Negative Lévy Models. The Annals of Applied Probability, Forthcoming.

N. Rodosthenous and M. Zervos (2017). Watermark options. Finance and Stochastics, Vol 21 (1), 157-186.

H. Zhang, N. Rodosthenous and O. Hadjiliadis (2015). Robustness of the N-CUSUM stopping rule in a Wiener disorder problem (2015). The Annals of Applied Probability, Vol 25 (6), 3405-3433.

**Seminars and meetings**

We are holding regular seminars Probability and Applications and Statistics at Queen Mary, cooperating with London Probability Seminar. Ilya Goldsheid is a co-organiser of The London Analysis and Probability Seminar

Members of the Group participated in the organisation of recent international meetings:

Classical and quantum motion in random environment. A random event in honour of Ilya Goldsheid’s 70th birthday. (Queen Mary, University of London, 18–22 December 2017)

Random and Other Ergodic Problems (Isaac Newton Inst., Cambridge 22 - 26 June 2015)

11th German Probability and Statistics Days (Ulm, 4 - 7 March 2014)

SPA 2013 (Boulder, 29/07- 2/08/2013 )

Paris-London Analysis Seminar (London, 28/03/2014)

13th Workshop on Stochastic Models, Statistics and their Applications (Berlin, February 2017)

Sixth International Workshop in Sequential Methodologies (Rouen, June 2017)

London-Paris Bachelier Workshop on Mathematical Finance, UCL, 09/2017

3rd Symposium Quantitative Finance and Risk Analysis, Corfu, 06/2017

Mathematical and Computational Finance Seminar, University of Oxford, 02/2017

Economic Theory Seminar, Bielefeld University, 01/2017

SIAM Conference on Financial Mathematics & Engineering, Austin Texas, 11/2016

**Editorial Activity**

Members of the Group are on the editorial boards of applied probability journals (AAP/JAP - Sasha Gnedin) general probability journals (Stochastics, Probability Surveys - Sasha Gnedin), and statistical journals (Sequential Analysis - Steve Coad, Journal of the Royal Statistical Society Series C. - Silvia Liverani).

**Grants**

Sasha Sodin is the PI of the ERC Start-Up Grant (2015-2020) "Spectral Theory of Random Operators"

John Moriarty is a holder of EPSRC Early Career Fellowship (2017-2020), working on the project "Markov chain optimisation for energy systems"

Neofytos Rodosthenous is a holder of a EPSRC First Grant (2017-2019), working on "Optimal timing for financial and economic decisions under adverse and stressful conditions"