First passage time distribution in heterogeneity controlled kinetics

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

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First passage time distribution in heterogeneity controlled kinetics : Going beyond the mean first passage time. / Godec, Aljaz; Metzler, Ralf.

In: Scientific Reports, Vol. 6, 20349, 08.02.2016.

Research output: Contribution to journal › Article › Scientific › peer-review

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@article{e9517bfa28ad4e4a815d78f582a47cd5,

title = "First passage time distribution in heterogeneity controlled kinetics: Going beyond the mean first passage time",

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.",

author = "Aljaz Godec and Ralf Metzler",

year = "2016",

month = "2",

day = "8",

doi = "10.1038/srep20349",

language = "English",

volume = "6",

journal = "Scientific Reports",

issn = "2045-2322",

publisher = "Nature Publishing Group",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - First passage time distribution in heterogeneity controlled kinetics

T2 - Going beyond the mean first passage time

AU - Godec, Aljaz

AU - Metzler, Ralf

PY - 2016/2/8

Y1 - 2016/2/8

N2 - 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.

AB - 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.

U2 - 10.1038/srep20349

DO - 10.1038/srep20349

M3 - Article

VL - 6

JO - Scientific Reports

JF - Scientific Reports

SN - 2045-2322

M1 - 20349

ER -

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