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Past events in this series

Thu, 07 Mar 2024

12:00 - 13:00

Short- and late-time behaviours of Fokker-Planck equations for heterogeneous diffusions

Ralf Blossey
(CNRS & University of Lille, France)

The Fokker-Planck equation is one of the major tools of statistical physics in the description of stochastic processes, with numerous applications in physics, chemistry and biology. In the case of heterogeneous diffusions, the formulation of the equation depends on the choice of the discretization of the stochastic integral in the underlying Langevin-equation due to the multiplicative noise. In the Fokker-Planck equation, the choice of discretization then enters as a parameter in the definition of drift and diffusion terms. I show how both short- and long-time limits are affected by this choice. In the long-time limit, the existence of normalizable probability distribution functions is not always guaranteed which can be remedied by invoking elements of infinite ergodic theory. 

[1] S. Giordano, F. Cleri, R. Blossey, Phys Rev E 107, 044111 (2023)

[2] T. Dupont, S. Giordano, F. Cleri, R. Blossey, arXiv:2401.01765 (2024)