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

Godec, A., & Metzler, R. (2016). First passage time distribution in heterogeneity controlled kinetics: Going beyond the mean first passage time. Scientific Reports, 6: 20349. doi:10.1038/srep20349.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-CB32-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-CB35-E
Genre: Journal Article

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Godec, A.1, Author              
Metzler, R., Author
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1Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_2396692              

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 Abstract: 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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Language(s): eng - English
 Dates: 2016-02-08
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1038/srep20349
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Title: Scientific Reports
Source Genre: Journal
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Pages: 11 Volume / Issue: 6 Sequence Number: 20349 Start / End Page: - Identifier: -