Diffusion with resetting in arbitrary spatial dimension

Abstract

We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state which exhibits non-Gaussian behaviour. We then consider the presence of an absorbing target centred at the origin and compute the survival probability and mean time to absorption of the diffusive particle by the target. The mean absorption time is finite and has a minimum value at an optimal resetting rate $r^{\ast }$ which depends on dimension. Finally we consider the problem of a finite density of diffusive particles, each resetting to its own initial position. While the typical survival probability of the target at the origin decays exponentially with time regardless of spatial dimension, the average survival probability decays asymptotically as $\exp -A(\log t{)}^d$ where $A$ is a constant. We explain these findings using an interpretation as a renewal process and arguments invoking extreme value statistics.

21 pages, 3 figures, submitted to Journal of Physics A

References in corpus (13)

• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Diffusion with Optimal Resetting
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Boosting search by rare events
• Stochastic multiplicative processes with reset events
• Monotonous continuous-time random walks with drift and stochastic reset events
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Switching and growth for microbial populations in catastrophic responsive environments
• Effect of Partial Absorption on Diffusion with Resetting
• Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps
• Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps

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