First passage time statistics of non-Markovian walkers: Onsager’s regression hypothesis approach
How long does it take for a random walker to reach its destination? Such a question on “first passage time” is fundamental in stochastic process, and relevant to many practical applications.
While the problem for the Markovian case (memory free) is well documented in literature, the presence of memory effect makes the standard analysis intractable, leaving many open questions in non-Markovian cases. We propose a method to think about the first passage statistics based on the non-equilibrium statistical mechanics idea, i.e., Onsager’s regression hypothesis, and demonstrate that it enables us to calculate various quantities of interest for non-Markovian systems analytically.
This work is in collaboration with Y. Sakamoto (Aoyama Gakuin University)
Reference: https://arxiv.org/abs/2301.13466
