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Open AccessFeature PaperArticle

Large Deviations for Continuous Time Random Walks

by Wanli Wang 1,2,*, Eli Barkai 1,2 and Stanislav Burov 1,*
1
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
2
Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
*
Authors to whom correspondence should be addressed.
Entropy 2020, 22(6), 697; https://doi.org/10.3390/e22060697
Received: 1 June 2020 / Revised: 15 June 2020 / Accepted: 17 June 2020 / Published: 22 June 2020
(This article belongs to the Special Issue New Trends in Random Walks)
Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory. View Full-Text
Keywords: large deviations; diffusing diffusivity; saddle point approximation; continuous time random walk; renewal process large deviations; diffusing diffusivity; saddle point approximation; continuous time random walk; renewal process
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Wang, W.; Barkai, E.; Burov, S. Large Deviations for Continuous Time Random Walks. Entropy 2020, 22, 697.

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