ABSTRACT:

We build up on previous works of Basile, Bernardin, Olla and Spohn, where a linear Boltzmann equation was obtained as the kinetic limit of a heat conduction model with conservative noise. We obtain the scaling limit of the energy fluctuations for this kinetic limit. When the conductivity is finite, the energy fluctuations are given by a Brownian motion, reflecting the diffusive nature of heat flow. In the remarkable case d=1, energy and momentum conserved, we obtain a Levy process of index 3/2, explaining why conductivity is infinite in that case. Joint work with T. Komorowski and S. Olla.