Seminário do Grupo de Física e Estatística - Rare events of small-noise Doob conditioned processes

Título: Rare events of small-noise Doob conditioned processes Resumo: Some of the most important things a noisy system can do, such as a protein folding into shape, a molecule crossing a reaction barrier, or a climate flipping between states, almost never happen on their own, which makes them extremely hard to sample in simulations. One way around this is Doob conditioning, where you shift the system so it is guaranteed to reach a chosen outcome, turning a rare event into a common one. The idea is that the exact shift force is almost never known. We show you do not need it in some cases, because conditioning is equivalent to just running the ordinary dynamics and keeping only the runs that happen to end where you want. In the weak noise limit, this reframing turns a hard statistical problem into a clean optimization one, locating the single most likely pathway a rare transition follows, and even how much heat it dissipates along the way. We illustrate the ideas on exactly solvable examples and on a minimal model of a molecule folding between two shapes.