Long time scaling behaviour for diffusion with resetting and memory

Abstract

We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory kernel, we show analytically how different asymptotic behaviours of the variance of the particle position emerge at long times. These range from standard diffusive (${\sigma }^2\sim t$) all the way to anomalous ultraslow growth ${\sigma }^2\sim \ln \ln t$.

13 pages, 1 figure, submitted to J. Stat. Mech: Theory. Exp

References in corpus (10)

• Diffusion under time-dependent resetting
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Diffusion with stochastic resetting at power-law times
• Random walks with preferential relocations to places visited in the past and their application to biology
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Random walk with random resetting to the maximum
• Solvable random walk model with memory and its relations with Markovian models of anomalous diffusion
• Slow Lévy flights
• Reinforced walks in two and three dimensions
• Ultraslow scaled Brownian motion

Cited by in corpus (46)

• Stochastic Resetting and Applications
• Run and tumble particle under resetting: a renewal approach
• First passage under stochastic resetting in an interval
• Stochastic resetting: A (very) brief review
• Quantum dynamics with stochastic reset
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Diffusion with resetting in a logarithmic potential
• First passage under restart with branching
• Localization transition induced by learning in random searches
• Non-renewal resetting of scaled Brownian motion
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Diffusion with stochastic resetting is invariant to return speed
• Ising model with stochastic resetting
• Transport properties and first arrival statistics of random searches with stochastic reset times
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process
• Invariants of motion with stochastic resetting and space-time coupled returns
• Continuous-time random walks with reset events: Historical background and new perspectives
• Intermittent resetting potentials
• Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
• Stochastic resetting by a random amplitude
• Local time of diffusion with stochastic resetting
• Stochastic processes subject to a reset-and-residence mechanism: transport properties and first arrival statistics
• Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting
• Diffusion with Resetting Inside a Circle
• The cost of stochastic resetting
• Number of distinct sites visited by a resetting random walker
• Diffusion with Partial Resetting
• Anderson-like localization transition of random walks with resetting
• Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes
• Exact extreme, order and sum statistics in a class of strongly correlated system
• Anomalous diffusion in random-walks with memory-induced relocations
• Random walks with preferential relocations and fading memory: a study through random recursive trees
• Dynamically emergent correlations between particles in a switching harmonic trap
• Critical number of walkers for diffusive search processes with resetting
• Non-linear diffusion with stochastic resetting
• Striking universalities in stochastic resetting processes
• Recurrence time correlations in random walks with preferential relocation to visited places
• Power-law relaxation of a confined diffusing particle subject to resetting with memory
• Unified approach to reset processes and application to coupling between process and reset
• Emerging correlations between diffusing particles evolving via simultaneous resetting with memory
• Diffusion with preferential relocation in a confining potential
• Ising Model with Power Law Resetting
• An exactly solvable predator prey model with resetting
• Large deviations principle for a stochastic process with random reinforced relocations
• Ultra slow sub-logarithmic diffusion of a sluggish random walker subject to resetting with memory