Berlin 2024 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 41: Statistical Physics: General
DY 41.1: Vortrag
Donnerstag, 21. März 2024, 09:30–09:45, BH-N 128
Survival probability of stochastic processes beyond persistence exponents — •Maxim Dolgushev — Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, 4 Place Jussieu, 75005 Paris, France
How long does it take a random walker to find a "target"? This time, called the first-passage time (FPT), appears in various domains: time taken by a predator to find its prey or by a transcription factor to find a specific sequence on the DNA, time taken by a virus to infect a cell or by a financial asset to exceed a certain threshold, time taken for the cyclization of a polymeric chain, etc.
From a theoretical point of view, a crucial parameter to evaluate FPTs is the possible presence of a geometrical confinement. For a symmetric random walk in a confined domain, the mean FPT ⟨ T⟩ is in general finite. The opposite case of unconfined random walks is radically different. In this case, either the walker has a finite probability of never finding the target (transient random walks), or he reaches it with probability one (recurrent random walks) and the probability of survival of the target decreases algebraically with time, S(t)∼ S0/tθ.
Our main result is a general exact relation for a process with stationary increments (more generally, for a process whose increments become stationary at long time only), Markovian or not, between the full asymptotic behavior (defined in the absence of confinement) and the mean FPT ⟨ T⟩ for the same process in a large confinement volume.
Keywords: random walks; first-passage time; survival probability; non-markovian processes