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  • Letter
  • Open Access

Doubly stochastic continuous time random walk

Maxence Arutkin1,2,* and Shlomi Reuveni1,3,†

  • 1School of Chemistry, Center for the Physics & Chemistry of Living Systems, Tel Aviv University, 6997801 Tel Aviv, Israel
  • 2Service d'Epidémiologie-Data-Biostatistiques, Délégation à la Recherche Clinique et à l'Innovation, Hôpital Foch, 92150 Suresnes, France
  • 3Sackler Center for Computational Molecular & Materials Science, Ratner Institute for Single Molecule Chemistry, Tel Aviv University, 6997801 Tel Aviv, Israel

  • *maxence@tauex.tau.ac.il
  • †shlomire@tauex.tau.ac.il
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Phys. Rev. Research 6, L012033 – Published 21 February, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012033

Abstract

Since its introduction some 60 years ago, the Montroll-Weiss continuous time random walk has found numerous applications due its ease of use and ability to describe both regular and anomalous diffusion. Yet, despite its broad applicability and generality, the model cannot account for effects coming from random diffusivity fluctuations, which have been observed in the motion of asset prices and molecules. To bridge this gap, we introduce a doubly stochastic version of the model in which waiting times between jumps are replaced with a fluctuating jump rate. We show that this newly added layer of randomness gives rise to a rich phenomenology while keeping the model fully tractable, allowing us to explore general properties and illustrate them with examples. In particular, we show that the model presented herein provides an alternative pathway to Brownian yet non-Gaussian diffusion, which has been observed and explained via diffusing diffusivity approaches.

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Phys. Rev. Research 6, L012033– Published 21 February, 2024
  • Received 13 February 2023
  • Accepted 23 January 2024
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