Infinite-dimensional stochastic differential equations related to Bessel random point fields
The authors study a system made of infinitely many Brownian particles on the line, interacting via a two-dimensional (i.e. logarithmic) Coulomb potential. They prove that the equilibrium states of the related stochastic dynamics are Bessel random point fields (BRPF). The result is obtained by proving a quasi-Gibbs property of the BRPF and by calculating their logarithmic derivative, which both turn out to be sufficient conditions for the existence of weak solutions to the dynamics.
infinite-dimensional stochastic differential equations
scientific article