We consider n such Brownian excursion paths conditioned to be nonintersecting. Using techniques from random matrix theory, we discuss this process. This is joint work with H. Widom.

3.15 Stochastic PDE

Organizer W.E. (Princeton)

3.15.1 Degenerately Forced Fluid Equations: Ergodicity and Solvable Models

Jonathan C. Mattingly

Duke University jonmmath.duke.edu

I will present some recent results on the existence of spectral gaps for the 2D Navier Stokes equation under very degenerate stochastic forcing. I will use these results to show that the statistical steady states depend in a nice fashion on the parameters of the problem.

I will close with some interesting results on some exactly solvable models of energy transport in stochastic systems.

3.15.2 Microscopic Stochastic Models for the Study of Thermal Conductivity

Stefano Olla

Université de Paris, Dauphine ollaceremade.dauphine.fr

Anomalous large thermal conductivity has been observed numerically and experimentally in oneand two-dimensional systems. We study the thermal conductivity of an infinite system of oscillators whose Hamiltonian dynamics is perturbed by a multiplicative (non-linear) noise conserving energy and momentum. The decay of the energy current correlation function C(t ) can be estimated. In the harmonic case C(t ) can be computed explicitly and we prove that thermal conductivity is finite if d = 3 or if an on-site potential is present, while it is infinite if d = 1 or 2. This result clarifies the role of conservation of momentum and dispersion relation in the anomalous thermal conductivity in low dimensions. We also discuss Fourier’s law and evolution of energy fluctuations. This is a joint work with Giada Basile and Cedric Bernardin.