Sébastien Dutercq - "Interface dynamics of a metastable mass-conserving diffusion"
We will consider a diffusion process defined by the stochastic differential equation $dx_t=-\nabla V_\gamma(x_t)dt+\sqrt(2\epsilon)dW_t$ where $V_\gamma$ is a potential with a conservation law and invariant under a group of symmetries. First we will describe the metastable states of the system, and then we will define a hierarchy on these metastable states. We will see how we can interpret the dynamics of this system in terms of the motion of its interfaces, and give sharp results on expected first-hitting times and its spectral gap.
