Spectral gap for measure-valued diffusion processes

Abstract

The spectral gap is estimated for some measure-valued processes, which are induced by the intrinsic/extrinsic derivatives on the space of finite measures over a Riemannian manifold. These processes are symmetric with respect to the Dirichlet and Gamma distributions arising from population genetics. In addition to the evolution of allelic frequencies investigated in the literature, they also describe stochastic movements of individuals.