Programme

Anyone interested is welcome. Some support may be available for the costs of travel and/or overnight stay. Please e-mail mrc@maths.warwick.ac.uk so that we can estimate the numbers involved.

ABSTRACTS

Andreas Eberle (Bonn) Convergence of sequential MCMC methods.
We study convergence properties of a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/ resampling schemes. We develop an analysis by funtional inequalities for an associated nonlinear flow of probability measures. This allows us to prove that the combined methods are sometimes converging rapidly in multimodal setups where traditional MCMC methods mix extremely slowly. For example, we can prove rapid convergence in the mean field Ising model at all temperatures.

Neil O'Connell (UC Cork) Interlaced random walks on the circle
We give a constructon which yields two or more interlaced sets of non-colliding random walks on the circle. The notions "interlacing" and "non-colliding" are closely related, in that there are some naturally associated operators which commute (a fact which plays a key role in the proof). I will also describe some connections with random tilings and a well-known result in random matrix theory on the super-position of two circular orthogonal ensembles. This talk is based on joint work with Tony Metcalfe and Jon Warren.

Martin Ondrejat ( Prague) Integral representations of martingales
History, applications, generalisations and the present state of art of the so called Doob representation theorem which characterises continuous martingales that are indefinite stochastic integrals with respect to a Wiener process.