Evolution of a passive particle in a one-dimensional diffusive environment
Huveneers, François; Simenhaus, François (2020), Evolution of a passive particle in a one-dimensional diffusive environment. https://basepub.dauphine.psl.eu/handle/123456789/22109
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Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-03071641Date
2020Series title
Cahier de recherche du CEREMADEPages
27
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Show full item recordAuthor(s)
Huveneers, FrançoisCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Simenhaus, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.Subjects / Keywords
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