Evidence and quantification of memory effects in competitive first-passage events.

ABSTRACT: Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian) processes. However, in complex systems such as polymer fluids, the motion of a particle should typically be described as a process with memory, for which splitting probabilities are much less characterized analytically. Here, we introduce an analytical approach that provides the splitting probabilities for one-dimensional isotropic non-Markovian Gaussian processes with stationary increments, in the case of two targets. This analysis shows that splitting probabilities are controlled by the out-of-equilibrium trajectories observed after the first passage. Th

SUBMITTER: Dolgushev M 

PROVIDER: S-EPMC11927618 | biostudies-literature | 2025 Mar

REPOSITORIES: biostudies-literature