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We consider an infinite system of non-overlapping globules undergoing Brownian motions in R-3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional stochastic differential equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.
We consider an infinite system of non overlaping globules undergoing Brownian motions in R3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinitedimensional Stochastic Differential Equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.
We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a pair potential with infinite range and quasi polynomial decay. It is modelized by an infinite-dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with deterministic initial condition. We also show that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential.
We consider a system of infinitely many hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional Stochastic Differential Equation with a local time term. We prove that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.
We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite- dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.
We consider a system of infinitely many hard balls in R<sup>d undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.