Abstract

In this talk, we study some stochastic differential equations related to continuous measurements of open quantum systems. In these equations, we consider the regime where the coefficient on the noise tends to infinity. Under some conditions, we get pure jump processes which correspond to continuous time Markov chains, these processes being decorated with spikes distributed like a Poisson point process. The proof of this result, which needs some work to be rigorously stated, uses the behaviour of the Brownian local time as one of its main tools. This is a joint work with Benoist, Bernardin, Chetrite, Chhaibi and Pellegrini.

Speaker

Joseph Najnudel is an Associate Professor at the University of Bristol. His research interests are random matrix theory and stochastic analysis.

Random matrix theory: study of random unitary matrices (in particular the Circular Unitary Ensemble), random permutation matrices and related infinite-dimensional limiting objects, link between random matrix theory and number theory, link between random matrix theory and mathematical physics.

Stochastic analysis: study of limiting measures constructed by modifying the Brownian motion or more general stochastic processes, study of the Brownian local times and polymer models.