Area under subdiffusive random walks

Fuente: arXiv
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Main Authors: Méndez, Vicenç, Flaquer-Galmés, Rosa, Cristín, Javier
Format: Preprint
Published: 2026
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author Méndez, Vicenç
Flaquer-Galmés, Rosa
Cristín, Javier
author_facet Méndez, Vicenç
Flaquer-Galmés, Rosa
Cristín, Javier
contents We study the statistical properties of the area and the absolute area under the trajectories of subdiffusive random walks. Using different frameworks to describe subdiffusion (as the scaled Brownian motion, fractional Brownian motion, the continuous-time random walk or the Brownian motion in heterogeneous media), we compute the first two moments, the ergodicity breaking parameter for the absolute area and infer a general scaling for the probability density functions of these functionals. We discuss the differences between the statistical properties of the area and the absolute area for the different subdiffusion models and illustrate the experimental interest of our results. Our theoretical findings are supported by Monte Carlo simulations showing an excellent agreement.
format Preprint
id arxiv_https___arxiv_org_abs_2602_04342
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Area under subdiffusive random walks
Méndez, Vicenç
Flaquer-Galmés, Rosa
Cristín, Javier
Statistical Mechanics
We study the statistical properties of the area and the absolute area under the trajectories of subdiffusive random walks. Using different frameworks to describe subdiffusion (as the scaled Brownian motion, fractional Brownian motion, the continuous-time random walk or the Brownian motion in heterogeneous media), we compute the first two moments, the ergodicity breaking parameter for the absolute area and infer a general scaling for the probability density functions of these functionals. We discuss the differences between the statistical properties of the area and the absolute area for the different subdiffusion models and illustrate the experimental interest of our results. Our theoretical findings are supported by Monte Carlo simulations showing an excellent agreement.
title Area under subdiffusive random walks
topic Statistical Mechanics
url https://arxiv.org/abs/2602.04342