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Propagation of dissipation in singular stochastic Hamiltonian systems

Banff International Research Station for Mathematical Innovation and Discovery

We discuss the problem of convergence to equilibrium in two SDEs: (1) underdamped Langevin dynamics and (2) the Nos\'{e}-Hoover equation under Brownian heating. In each system, the invariant probability distribution has an explicit density which is known up to a normalization constant. Moreover, each density is of the Boltzmann-Gibbs form. In the context of statistical sampling, this form is exploited in order to take samples from a wide array of probability distributions by running the stochastic dynamics "long enough" when started from conveniently chosen prior distributions. However, outside of a particular class of target distributions, comparably little is known about how fast the stochastic dynamics converges to this equilibrium. This talk will cover joint work with my collaborators to bridge this gap, especially in the context of the singular, Lennard-Jones interaction potential.

Mathematics; Probability Theory And Stochastic Processes; Global Analysis; Analysis On Manifolds

video/mp4

Author affiliation: Iowa State University

2021-09-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/79663

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/