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Evolution of a passive particle in a one-dimensional diffusive environment
Publication type: Journal Article
Publication date: 2023-01-01
scimago Q1
wos Q3
SJR: 1.355
CiteScore: 1.9
Impact factor: 1.1
ISSN: 10836489
Statistics and Probability
Statistics, Probability and Uncertainty
Abstract
We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time limit, we show that the fluctuations of the particle become Gaussian and sub-diffusive, with dynamical exponent 3∕4. Second, in the long time limit, we show that the particle is trapped by the local minima of the potential and evolves diffusively i.e. with exponent 1∕2.
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Huveneers F., Simenhaus F. Evolution of a passive particle in a one-dimensional diffusive environment // Electronic Journal of Probability. 2023. Vol. 28. No. none.
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Huveneers F., Simenhaus F. Evolution of a passive particle in a one-dimensional diffusive environment // Electronic Journal of Probability. 2023. Vol. 28. No. none.
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TY - JOUR
DO - 10.1214/22-ejp896
UR - https://doi.org/10.1214/22-ejp896
TI - Evolution of a passive particle in a one-dimensional diffusive environment
T2 - Electronic Journal of Probability
AU - Huveneers, François
AU - Simenhaus, François
PY - 2023
DA - 2023/01/01
PB - Institute of Mathematical Statistics
IS - none
VL - 28
SN - 1083-6489
ER -
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BibTex (up to 50 authors)
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@article{2023_Huveneers,
author = {François Huveneers and François Simenhaus},
title = {Evolution of a passive particle in a one-dimensional diffusive environment},
journal = {Electronic Journal of Probability},
year = {2023},
volume = {28},
publisher = {Institute of Mathematical Statistics},
month = {jan},
url = {https://doi.org/10.1214/22-ejp896},
number = {none},
doi = {10.1214/22-ejp896}
}