# 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…

## 17 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

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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

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- 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

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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.

- 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…

### 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 tm at which the process reaches the global maximum within the time interval [0, T ]. By using a…

### 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…

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

- Physics
- 2022

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…

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