# Fractional kinetics equation from a Markovian system of interacting Bouchaud trap models

Source: [Fractional kinetics equation from a Markovian system of interacting Bouchaud trap models](<https://www.sota2.com/research/paper/68fa48681e209131ce92f7aa>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T04:33:06.473Z

Authors: Alberto Chiarini, Simone Floreani, Federico Sau

Published: 2023-02-20T18:41:28.000Z

## Abstract

We consider a partial exclusion process evolving on $\\mathbb Z^d$ in a random trapping environment. In dimension $d\\ge 2$, we derive the fractional kinetics equation \\begin{equation\*}\\frac{\\partial^\\beta\\rho\_t}{\\partial t^\\beta} = \\Delta \\rho\_t   \\end{equation\*} as a hydrodynamic limit of the particle system. Here, $\\frac{\\partial^\\beta}{\\partial t^\\beta}$, $\\beta\\in(0,1)$, denotes the fractional derivative in the Caputo sense. We thus exhibit a Markovian interacting particle system whose empirical density field rescales to a sub-diffusive equation corresponding to a non-Markovian process, the Fractional Kinetics process. In contrast, we show that, when $d=1$, the system rescales to the solution to \\begin{equation\*}   \\frac{\\partial \\rho\_t}{\\partial t}= \\mathcal L\_\\beta \\rho\_t\\ , \\end{equation\*} where $\\mathcal L\_\\beta$ is the random generator of the singular quasi-diffusion known as FIN diffusion.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2302.10156>)

[PDF](<https://arxiv.org/pdf/2302.10156.pdf>)