# Characterization of stationary states in random walks with stochastic resetting.

@article{Mndez2016CharacterizationOS, title={Characterization of stationary states in random walks with stochastic resetting.}, author={Vicenç M{\'e}ndez and Daniel Campos}, journal={Physical review. E}, year={2016}, volume={93 2}, pages={ 022106 } }

It is known that introducing a stochastic resetting in a random-walk process can lead to the emergence of a stationary state. Here we study this point from a general perspective through the derivation and analysis of mesoscopic (continuous-time random walk) equations for both jump and velocity models with stochastic resetting. In the case of jump models it is shown that stationary states emerge for any shape of the waiting-time and jump length distributions. The existence of such state entails…

## 57 Citations

### Transport properties of random walks under stochastic noninstantaneous resetting.

- MathematicsPhysical review. E
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This work introduces noninstantaneous resetting as a two-state model being a combination of an exploring state where the walker moves randomly according to a propagator and a returning state whereThe walker performs a ballistic motion with constant velocity towards the origin.

### Continuous-time random walks under power-law resetting.

- MathematicsPhysical review. E
- 2020

It is shown, that the behavior of the MSD is the same as in the scaled Brownian motion (SBM), being the mean-field model of the CTRW, and the intermediate asymptotics of the probability density functions for CTRW under complete resetting (provided they exist) are also the same.

### 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}.

### Symmetric exclusion process under stochastic resetting.

- MathematicsPhysical review. E
- 2019

While the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behavior.

### Random acceleration process under stochastic resetting

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- 2020

We consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism. Denoting the position and velocity by x and v respectively, we consider two different…

### Nonrenewal resetting of scaled Brownian motion.

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- 2019

We investigate an intermittent stochastic process in which diffusive motion with a time-dependent diffusion coefficient, D(t)∼t^{α-1}, α>0 (scaled Brownian motion), is stochastically reset to its…

### Stochastic resetting and applications

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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…

### Work Fluctuations and Jarzynski Equality in Stochastic Resetting.

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It is shown that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event.

### Invariants of motion with stochastic resetting and space-time coupled returns

- MathematicsNew Journal of Physics
- 2019

Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time…

### Non-linear diffusion with stochastic resetting

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a…

## References

SHOWING 1-10 OF 11 REFERENCES

### ET

- HistoryProceedings of the 22nd International Conference on World Wide Web - WWW '13 Companion
- 2013

. — The holotype of Proctotretus signifer Dum. et Bibr., 1837, considered as lost since 1851, has been found again in the Paris Museum material that was catalogued as a type-series of P. fitzingerii…

### Phys

- Rev. E 92, 062115
- 2015

### Rev

- Mod. Phys. 83, 81
- 2011

### Phys

- Rev. E 82, 061112
- 2010

### Phys

- Rev. E 87, 012116
- 2013

### A: Math

- Theor. 47, 285001
- 2014

### Phys

- Rev. Lett. 113, 220602
- 2014

### Proc

- Natl. Acad. Sci. USA 105, 4633
- 2008

### Phys

- Rev. E 55, 99
- 1997

### Phys

- Rev. E 91, 052131
- 2015