First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time

  • The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening series of new results focusing mostly on the so-called mean and global first passage time (MFPT and GFPT, respectively) of such processes. Here we push the understanding of first passage processes one step further. For a simple heterogeneous system we derive rigorously the complete distribution of first passage times (FPTs). Our results demonstrate that the typical FPT significantly differs from the MFPT, which corresponds to the long time behaviour of the FPT distribution. Conversely, the short time behaviour is shown to correspond to trajectories connecting directly from the initial value to the target. Remarkably, we reveal a previously overlooked third characteristic time scale of the first passage dynamics mirroring brief excursion away from the target.

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Author:Aljaz Godec, Ralf Metzler
Pubmed Id:
Parent Title (English):Scientific reports
Publisher:Nature Publ. Group
Place of publication:London
Document Type:Article
Year of first Publication:2016
Year of Completion:2016
Release Date:2020/03/22
Funder:Alexander von Humboldt Fellowship; ARRS programme [P1-0002]; Academy of Finland (Suomen Akatemia) within the Finland Distinguished Professor scheme
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert