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Statistical distributions as stationary measures of stochastic-dynamical systems: formulation, numerical integrators, and applications

Tuesday, November 15, 2011
3:30PM – 5PM
POB 6.304

Ben Leimkuhler, School of Mathematics, University of Edinburgh

I will discuss degenerate diffusions for sampling Gibbs (i.e smooth)
measures. While familiar methods such as Langevin dynamics have proven to be reliable performers in some types of applications, they can be less desirable in treating problems with a complicated structure. I will show that it is often possible to use Ornstein-Uhlenbeck processes (avoiding the introduction of multiplicative noise) and to obtain in this way simplified results on the invariant measure of numerical methods. I will also discuss the treatment of constrained measures, including isoenergetic, isokinetic and other cases. Applications will include a study of the Hamiltonian vortex method in which the energetic interactions with a bath of weak vortices are treated as thermal fluctuations.

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