Fractional Brownian motion in presence of two fixed adsorbing boundaries

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dc.creatorOshanin, G.
dc.date2008-01-04
dc.date.accessioned2026-07-07T08:52:36Z
dc.date.available2026-07-07T08:52:36Z
dc.descriptionWe study the long-time asymptotics of the probability P_t that the Riemann-Liouville fractional Brownian motion with Hurst index H does not escape from a fixed interval [-L,L] up to time t. We show that for any H \in ]0,1], for both subdiffusion and superdiffusion regimes, this probability obeys \ln(P_t) \sim - t^{2 H}/L^2, i.e. may decay slower than exponential (subdiffusion) or faster than exponential (superdiffusion). This implies that survival probability S_t of particles undergoing fractional Brownian motion in a one-dimensional system with randomly placed traps follows \ln(S_t) \sim - n^{2/3} t^{2H/3} as t \to \infty, where n is the mean density of traps.
dc.description13 pages, submitted to J.Phys.A
dc.identifierhttps://arxiv.org/abs/0801.0676
dc.identifierhttp://arxiv.org/abs/0801.0676
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145332
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.titleFractional Brownian motion in presence of two fixed adsorbing boundaries
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