Large deviation principle for a stochastic process with random reinforced relocations

Boci, Erion-Stelios; Mailler, Cécile

doi:10.1088/1742-5468/aceb50

Cited by 2 publications

(2 citation statements)

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“…where λ ⩾ 0 is a constant independent of x and t. Note that the space-dependent function ϕ(x) is independent of r and satisfies the same eigenvalue equation (10) as the r = 0 case. Consequently, the analysis of the spatial part is exactly as in the r = 0 case discussed in the previous section.…”

Section: J Stat Mech (2024) 073206mentioning

confidence: 99%

“…Various other generalisations of this simple model have been studied in the recent past, for instance by considering a decaying memory [6], Lévy flights [7] or active particles [8]. A central limit theorem and an anomalous large deviation principle have also been established for a class of memory walks of this type, for a broad range of memory kernels [9,10]. The rigorous proofs of these latter results are based on a connection between the resetting process to previous sites and the growth of weighted random recursive trees.…”

Section: Introductionmentioning

confidence: 99%

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Power-law relaxation of a confined diffusing particle subject to resetting with memory

Boyer,

Majumdar

2024

J. Stat. Mech.

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We study the relaxation of a Brownian particle with long range memory under confinement in one dimension. The particle diffuses in an arbitrary confining potential and resets at random times to previously visited positions, chosen with a probability proportional to the local time spent there by the particle since the initial time. This model mimics an animal which moves erratically in its home range and returns preferentially to familiar places from time to time, as observed in nature. The steady state density of the position is given by the equilibrium Gibbs–Boltzmann distribution, as in standard diffusion, while the transient part of the density can be obtained through a mapping of the Fokker–Planck equation of the process to a Schrödinger eigenvalue problem. Due to memory, the approach at late times toward the steady state is critically self-organised, in the sense that it always follows a sluggish power-law form, in contrast to the exponential decay that characterises Markov processes. The exponent of this power-law depends in a simple way on the resetting rate and on the leading relaxation rate of the Brownian particle in the absence of resetting. We apply these findings to several exactly solvable examples, such as the harmonic, V-shaped and box potentials.

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Section: J Stat Mech (2024) 073206mentioning

confidence: 99%