Celebratio Mathematica — Varadhan

Large deviations

Works connected to Jeremy Quastel

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J. Quastel, F. Rezakhanlou, and S. R. S. Varadhan: “Large deviations for the symmetric simple exclusion process in dimensions \( d\geq 3 \),” Probab. Theory Related Fields 113 : 1 (1999), pp. 1–84. MR 1670733 Zbl 0928.60087 article

We consider symmetric simple exclusion processes with \( L=\overline{\rho}N^d \) particles in a periodic \( d \)-dimensional lattice of width \( N \). We perform the diffusive hydrodynamic scaling of space and time. The initial condition is arbitrary and is typically far away form equilibrium. It specifies in the scaling limit a density profile on the \( d \)-dimensional torus. We are interested in the large deviations of the empirical process, \[ N^{-d}\Bigl[\sum_1^L\delta_{x_i(\,\cdot\,)}\Bigr] \] as random variables taking values in the space of measures on \( D[0,1] \). We prove a large deviation principle, with a rate function that is more or less universal, involving explicitly besides the initial profile, only such canonical objects as bulk and self diffusion coefficients.

Fraydoun Rezakhanlou	Related
Jeremy Quastel	Related