Interacting Brownian Particles

This book studies well-posedness of multidimensional stochastic differential equations (SDEs) driven by Brownian motion and with irregular coefficients, i.e., the coefficients are not assumed to be continuous and globally Lipschitz. Such singular stochastic equations are usually not included in the standard theory of stochastic calculus. As an application we will prove existence and uniqueness of solutions for a stochastic model proposed by the theoretical physicist Dyson in 1962. This model deals with the interaction of n particles in a Coulomb gas; indeed one considers n points charges executing Brownian motion under their mutual electrostatic repulsion; one can proceed until finding an equation which describes the motion of those particles.