## Members of the Probability and Applications Group: some thumbnail sketches

Steve Coad'sinterests are mainly in the area of sequential analysis, with particular emphasis on estimation following sequential tests, models for multi-armed clinical trials, response-adaptive designs, multivariate analysis, adaptive nonlinear regression models, asymptotic approximations, models for early phase clinical trials and inference following biased coin designs. This research is motivated by issues arising in clinical trials, such as: if we use adaptive treatment allocation, how do we carry out a valid analysis? Some of the theoretical work leads to results which have applications in other areas. | |

Alexander Gnedin is doing research on combinatorial models of applied probability and their connection with continuous-time and space random processes like Brownian motion and Levy processes. He contributed to the area of stochastic optimisation, in particular optimal stopping and online sequential selection problems. He worked on applications of the renewal theory to partition-valued processes of random fragmentation and coalescence, and on big-sample asymptotics in the classic models of occupancy. He is currently interested in random combinatorial structures with various kinds of sufficiency or stochastic symmetry; these are forming a sustainable bridge from the theoretical constructions to concrete problems, where the toolbox of researchers and practitioners has been fundamentally constrained by the paradigm of uniform distribution. | |

Ilya Goldsheid's research interests lie mainly in probability theory and mathematical physics. More specifically but still in broad terms, they could be described as the study of quantum and classical dynamics in random media. Finally in much more precise terms, he is interested in the celebrated localization problem for the Anderson model, i.e. quantum particles in random media, and in the study of random walks in random environments, as models for classical particles in random media. His other interests include products of random matrices, Lyapunov exponents of products random transformations, spectral properties of non-self-adjoit random operators. Some of the latter topics are motivated by the study of the localization problem and random walks; at the same time all of them are of great importance in their own right. | |

Jamie Griffin's main research area is modelling malaria transmission and control. This has involved synthesising multiple types of data to be able to make predictions of the impact of interventions in reducing malaria transmission, and to estimate and communicate the uncertainty in these predictions to decision makers at the WHO and elsewhere. He is also interested in statistical inference for infectious disease models more generally, which has included both theoretical aspects and practical work, for example on meningitis in the Sahel and influenza. | |

Boris Khoruzhenko has research interests at the interface of the theory of disordered systems and random matrices and their applications. Together with Yan Fyodorov and Hans-Juergen Sommers he discovered the regime of weak non-Hermiticity in the complex spectra and studied the crossover from Wigner-Dyson to Ginibre eigenvalue statistics for complex matrices. This work, motivated by applications to open quantum chaotic systems was awarded prize (and a medal) by the Institute Henri Poincaré (Paris) in 1998. More recently, together with Ilya Goldsheid, Boris developed a theory explaining why tridiagonal random matrices have eigenvalues lying on curves in the complex plane and describing fine properties of the eigenvalue distribution. This work was motivated by non-Hermitian quantum mechanics of Hatano and Nelson. Currently he is researching in the applications of the theory of symmetric polynomials, and in particular Schur functions and associated character expansions, to problems of the Random Matrix Theory. | |

Malwina Luczak's main research interests lie in the area of Markov chains, with particular emphasis on their long-term behaviour (e.g. speed of convergence of equlibrium, properties of the stationary distribution, quasi-stationarity). She is also interested in understanding phase transitions in random graphs. The practical motivation for her research comes from a desire to understand the spread of epidemic in large populations, as well as the behaviour of large communication networks. | |

Hugo Maruri-Aguilar's research interests lie in design of experiments, and within this broad subject, He has worked on two main areas: algebraic techniques in design of experiments and design and analysis of computer experiments. A design topic that has attracted his attention recently is the application of design of experiments for music and audio information retrieval. This stems as part of joint collaboration with colleagues in the School of Electronic Engineering and Computer Science (EECS) in Queen Mary. Other topics of interest are factor screening and model selection techniques such as lasso; cluster analysis and likelihood-based inference. | |

John Moriarty is an EPSRC early career research fellow jointly funded by the Mathematics and Energy themes. He is an applied probabilist, interested in theoretical questions of continuous time stochastic control and optimisation, and methods of computationally intensive statistics. In applications his interests include questions of the planning, design and operation of energy infrastructure and markets, and the interaction between the two. He also works across academic disciplines and with industry, for example developing real options models and algorithms for the optimal real-time operation of demand response. | |

Neofytos Rodosthenous' research interests in financial mathematics are mainly driven by problems of stochastic analysis, stochastic control and optimisation, optimal stopping and free-boundary problems, stochastic games, sequential testing and change-point detections, also known as disorder problems. The financial applications arising from the aforementioned mathematical problems include among others the pricing of American contingent claims, investment decision making and the quickest detection of abrupt changes in streams of ﬁnancial data. |