Equilibrium Fluctuations for an Interacting Brownian Particles Process

C. Tremoulet

2004, v.10, №2, 191-215


In this paper, we study the equilibrium fluctuations for an interacting Brownian particles process. The interaction between particles is given by a two-body superstable potential. The result is old and it is due to Spohn, [H. Spohn, Equilibrium fluctuations for interacting Brownian particles, Commun. Math. Phys., 1986, v. 103, 1-33]. He proved that the time-dependent density fluctuations field converges in law to the solution of a stochastic partial differential equation driven by white noise. In this paper, we give a new and simpler proof introduced by Chang in [C.-C. Chang, Equilibrium fluctuations of gradient reversible particles systems, Probab. Theory and Relat. Fields, 1994, v. 100, 269-283]. Moreover, in [R. Lang, Unendlich-dimensionale Wienerprozesse mit Wechselwirkung Teil I, Z. Wahrsch. verw. Geb., 1977, v. 38, 819-834], the existence of the dynamics of the process is proven. But, in this paper, we also add a new and less difficult proof of the existence of the dynamics at equilibrium.

Keywords: interacting particles process,equilibrium fluctuations,bulk diffusion


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