## Abstract

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.

Original language | English |
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Article number | 697 |

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Entropy |

Volume | 22 |

Issue number | 6 |

DOIs | |

State | Published - 22 Jun 2020 |

### Bibliographical note

Publisher Copyright:©2020 by the authors. Licensee MDPI, Basel, Switzerland.

### Funding

Funding: E.B. acknowledges the Israel Science Foundations grant 1898/17 and S.B. is supported by the Pazy foundation grant 61139927.

Funders | Funder number |
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Israel Science Foundations | 1898/17, 61139927 |

## Keywords

- Continuous time random walk
- Diffusing diffusivity
- Large deviations
- Renewal process
- Saddle point approximation