University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > A pathwise approach to relativistic diffusions

A pathwise approach to relativistic diffusions

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If you have a question about this talk, please contact Prof. Mihalis Dafermos.

A new class of relativistic diffusions encompassing all the previously studied examples has recently been introduced by C. Chevalier and F. Debbasch, both in a heuristic and analytic way. Roughly speaking, they are characterised by the existence at each (proper) time (of the moving particle) of a (local) rest frame where the random part of the acceleration of the particle (computed using the time of the rest frame) is Brownian in any spacelike direction of the frame.

I will explain how the tools of stochastic calculus enable us to give a concise and elegant description of these random paths on any Lorentzian manifold. A mathematically clear definition of the one-particle distribution function of the dynamics will emerge from this definition, and whose main property will be explained. This will enable me to obtain a general H-theorem and to shed some light on links between probabilistic notions and the large scale structure of the manifold.

All necessary tools from stochastic calculus will be explained.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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