A Law of Large Numbers for an Interacting Particle System with Confining Potential

Details A Law of Large Numbers for an Interacting Particle System with Confining Potential A Law of Large Numbers for an Interacting Particle System with Confining Potential

2007-01-03

arxiv.org/abs/math/0701095v1

Mathematics

Probability

29 pages

Scientific paper

In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction potential modeling the interaction among all the particles of the system. The limiting behavior as the size $N$ grows to infinity is achieved as a law of large numbers for the empirical process associated with the interacting particle system

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