ANAP Seminar | Speaker: Leander Schnee, (Freie Universität Berlin).

Venue: Sala de Seminários Ed.6-3.08, Campus de Gualtar

Online: Link  

Abstract: We consider the scaling limit of the fluctuations at equilibrium of a chain of oscillators with exponential Hamiltonian together with a conservative symmetric noise. Scaling the time by $n^2$ and the asymmetric Hamiltonian by $n^{-1/2}$ it is known that the equilibrium fluctuations converge to the energy solutions of the stochastic Burgers equation (SBE). 
We investigate a way to get a boundary condition for this limiting SPDE by adding a moving heat bath scaled by $n^{-\delta}$ to the particle dynamics. We show that for $\delta\leq 1$ the fluctuation field converges to SBE with one Dirichlet boundary. The boundary condition is exhibited through the use of different test functions depending on the different values of $\delta$. For $\delta<1$ we see SBE on R without a boundary.

This is a joint work in progress with Cédric Bernardin, Ana Djurdjevac and Patrícia Gonçalves.