Mathis Gueneau

Large Deviations in Switching Diffusion: Dynamical Condensation and Diffusivity BBP Transition

We consider a Brownian particle with position $x(t)$ whose diffusivity changes at Poissonian switching times, with each new value drawn independently from a bounded distribution $W(D)$. Assuming $W(D)\sim C(D_{\max}-D)^\nu$ near its upper edge, we study the large-deviation regime $x(t)\simeq yt$ with $y = O(1)$ at larg...