Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests

@article{Faisant2021OptimalMF,
  title={Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests},
  author={F{\'e}lix Faisant and Benjamin Besga and A. N. Petrosyan and Sergio Ciliberto and Satya N. Majumdar},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2021},
  volume={2021}
}
We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius R tol, a target at a distance L from an initial position in the presence of resetting. The reset position is Gaussian distributed with width σ. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first… 

Discrete space-time resetting model: application to first-passage and transmission statistics

We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability

Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes

During a random search, resetting the searcher’s position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have

Large time probability of failure in diffusive search with resetting in arbitrary dimension--a functional analytic approach

. We consider a stochastic search model with resetting for an unknown stationary target a ∈ R d , d ≥ 1, with known distribution µ . The searcher begins at the origin and performs Brownian motion

Winding number of a Brownian particle on a ring under stochastic resetting

  • Pascal Grange
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
We consider a random walker on a ring, subjected to resetting at Poisson-distributed times to the initial position (the walker takes the shortest path along the ring to the initial position at

First-passage time of run-and-tumble particles with noninstantaneous resetting.

We study the statistics of the first-passage time of a single run-and-tumble particle (RTP) in one spatial dimension, with or without resetting, to a fixed target located at L>0. First, we compute

First-passage Brownian functionals with stochastic resetting

We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A first-passage functional is defined as

Time to reach the maximum for a stationary stochastic process

We consider a one-dimensional stationary time series of fixed duration T . We investigate the time tm at which the process reaches the global maximum within the time interval [0, T ]. By using a

Diffusion with partial resetting

Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were

Freezing transitions of Brownian particles in confining potentials

We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential v(x) in a finite domain. We focus on the cases in which the

Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting

We study the fluctuations of the area A(t)=∫0tx(τ)dτ under a self-similar Gaussian process x(τ) with Hurst exponent H > 0 (e.g., standard or fractional Brownian motion, or the random acceleration

References

SHOWING 1-10 OF 82 REFERENCES

Optimal mean first-passage time for a Brownian searcher subjected to resetting: Experimental and theoretical results

The optimal mean first-passage time as a function of the resetting period/rate for different values of the ratio b = L/$\sigma$ is studied and an interesting phase transtion at a critical value b = bc is found.

Diffusion with optimal resetting

We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider

Diffusion with resetting in arbitrary spatial dimension

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

First-passage statistics under stochastic resetting in bounded domains

We investigate the first-passage problem where a diffusive searcher stochastically resets to a fixed position at a constant rate in a bounded domain. We put forward an analytical framework for this

Diffusion under time-dependent resetting

We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We

First Order Transition for the Optimal Search Time of Lévy Flights with Resetting.

An intermittent search process in one dimension where a searcher undergoes a discrete time jump process starting at x_{0}≥0 and the mean first passage time (MFPT) to the origin is studied, which has a global minimum in the (μ,r) plane.

Transport properties and first-arrival statistics of random motion with stochastic reset times.

This work studies the existence of a finite equilibrium mean-square displacement (MSD) when resets are applied to random motion with 〈x^{2}(t)〉_{m}∼t^{p} for 0<p≤2}.

First passage under stochastic resetting in an interval.

A comprehensive study of the first-passage properties of the Brownian particle diffusing in a one-dimensional interval with absorbing end points and shows how this set-up is a manifestation of a success-failure problem.

Diffusion with stochastic resetting.

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian

Dynamical phase transition in the first-passage probability of a Brownian motion.

A very good agreement is found between theoretical predictions and experimental results obtained with a Brownian bead whose diffusion is initialized by an optical trap which determines the initial distribution g(x_{0}/σ), and this transition is robust.
...