Celebratio Mathematica — Varadhan

Varadhan's work on hydrodynamical limits

Works connected to Monroe D. Donsker

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M. D. Donsker and S. R. S. Varadhan: “Large deviations from a hydrodynamic scaling limit,” Comm. Pure Appl. Math. 42 : 3 (April 1989), pp. 243–270. MR 982350 Zbl 0780.60027 article

The problem of describing how a large system evolves towards its equilibrium in terms of the evolution of certain macroscopic quantities can be formulated and studied in widely different contexts. Recently in [Guo, Papanicolaou and Varadhan 1988] one such model has been studied using estimates based on entropy and its rate of change. The main result in [Guo, Papanicolaou and Varadhan 1988] is a law of large numbers type result which asserts that the macroscopic functions evolve according to a specific deterministic motion (to be more specific a nonlinear diffusion equation) as the size gets large and the fluctuations disappear in the scaling. The present article is a complement to [Guo, Papanicolaou and Varadhan 1988] and we are interested here in estimating precisely the probabilities of significant (large) deviations from the deterministic limit. A similar result in a different context has been derived in [Kipnis, Olla and Varadhan 1989].