# 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…

## 19 Citations

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

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

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

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

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

- Mathematics
- 2021

. 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

- MathematicsJournal 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…

### Optimal Resetting Brownian Bridges via Enhanced Fluctuations.

- MathematicsPhysical review letters
- 2022

We introduce a resetting Brownian bridge as a simple model to study search processes where the total search time t_{f} is finite and the searcher returns to its starting point at t_{f}. This is…

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

- MathematicsPhysical review. E
- 2022

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

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

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…

### Diffusion with partial resetting.

- MathematicsPhysical review. E
- 2022

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

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

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…

### Time to reach the maximum for a stationary stochastic process.

- MathematicsPhysical review. E
- 2022

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

## References

SHOWING 1-10 OF 82 REFERENCES

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

- Computer Science
- 2020

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

- Mathematics
- 2011

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…

### Stochastic Search with Poisson and Deterministic Resetting

- Mathematics
- 2016

Deterministic resetting typically leads to a lower search cost than in stochastic resetting, and several unexpected feature arise for searchers when the resetting is deterministic, including the search time being independent of $T$ for $1/T\to 0$ and the search cost being independentof $N$ over a suitable range of $N$.

### Diffusion with resetting in arbitrary spatial dimension

- Mathematics
- 2014

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…

### Stochastic resetting and applications

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose…

### Diffusion under time-dependent resetting

- Mathematics
- 2015

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.

- MathematicsPhysical review letters
- 2014

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.

- MathematicsPhysical review. E
- 2019

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.

- MathematicsPhysical review. E
- 2019

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.

- Physics, MathematicsPhysical review letters
- 2011

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…