Georgia Institute of Technology College of Sciences

Quasi-stationary distributions (QSDs) are those almost invariant to a diffusion process over exponentially long time. Representing important transient stochastic dynamics, they arise frequently in applications especially in chemical reactions and population systems admitting extinction states. This talk will present some rigorous results on the existence, uniqueness, concentration, and convergence of QSDs along with their connections to the spectra of the Fokker-Planck operators.