Mathematical models in the population dynamics are dealing with the special class of the infinite dimensional Markov processes. Their phase space is a set of all locally finite configurations of the points (particles) in. Dynamics of such configurations includes the birth and death of particles and their random motion (diffusion, jumps etc.). The goal of the theory is to give the conditions of the ergodicity of such systems and explain several well-known empirial facts, for instance, the high level of mom-uniformity in the spatial distribution of the particles ("patches").
The talk will contain a review of the recent results in this area and the open problems.
Two Results in Probability Theory