Large deviations and scaling limit. (English) Zbl 1185.60024

Varadhan, Srinivasa R. S.

Lett. Math. Phys. 88, No. 1-3, 175-185 (2009).

The behavior of large systems is investigated under scaling limits, by employing methods from the theory of large deviations. Scaling limits deal with large systems whose evolution is modeled at a microscopic level by suitable stochastic differential equations and which are amenable to a statistical description in terms of (macroscopic) partial differential equations. The considered large systems stay away from any global equilibrium. The basic aim of the paper is to study such system at a time scale where it reaches equilibria locally, even though they still vary in space and time. The microscopic noisy evolution appears to be important in stabilizing the large system and keeping it in the vicinity of local equillibria.

Reviewer: Piotr Garbaczewski (Opole)

MSC:

60F10	Large deviations
60J60	Diffusion processes
37H15	Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
76R50	Diffusion
82C31	Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics

Keywords:

large deviations; scaling limits; random perturbations of dynamical systems; local equilibria; stability compressible Euler equation; tagged particle diffusion

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