First passage under stochastic resetting in an interval

Pal, A.; Prasad, V.

doi:10.1103/physreve.99.032123

Cited by 156 publications

(162 citation statements)

References 56 publications

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“…Moreover, starting from Eq. (19), we find that as the system is cooled down from a high temperature the transition gives rise to a diverging time scale…”

Section: Discussionmentioning

confidence: 84%

Péclet number governs transition to acceleratory restart in drift-diffusion

Ray¹,

Mondal²,

Reuveni³

2019

J. Phys. A: Math. Theor.

109

105

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First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the Péclet number (Pe) -the ratio between the rates of advective and diffusive transport. When Pe > 1 the process is drift-controlled and restart can only hinder its completion. In contrast, when 0 ≤ Pe < 1 the process is diffusion-controlled and restart can speed-up its completion by a factor of ∼ 1/Pe. Such speedup occurs when the process is restarted at an optimal rate r r 0 (1 − Pe), where r 0 stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions -some of its central features are completely generic. arXiv:1811.08239v4 [cond-mat.stat-mech]

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“…Moreover, starting from Eq. (19), we find that as the system is cooled down from a high temperature the transition gives rise to a diverging time scale…”

Section: Discussionmentioning

confidence: 84%

Péclet number governs transition to acceleratory restart in drift-diffusion

Ray¹,

Mondal²,

Reuveni³

2019

J. Phys. A: Math. Theor.

109

105

View full text Add to dashboard Cite

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“…Similarly, one can also find several studies where stochastic resetting mechanism is imposed in Refs. [36,37,38,39,40,41,42,43]. Recently, some investigations are also devoted in understanding the large deviation function of the observable of the Markov processes with stochastic resetting, and connection of stochastic thermodynamics [44,45,46] and resetting [47].…”

Section: Introductionmentioning

confidence: 99%

Stochastic resetting in underdamped Brownian motion

Gupta¹

2019

J. Stat. Mech.

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We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate r whereas its velocity evolves irrespective of the position of the particle and stochastic resetting mechanism. The nonequilibrium steady state of the position distribution is studied for this model system. Further, we study the distribution of the position of the particle in the finite time and the approach to the nonequilibrium steady state distribution with time. Numerical simulations are done to verify the analytical results.

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“…The simple model of diffusion with stochastic resetting has been extended and generalized to cover: diffusion in the presence of a potential [6][7][8], in a domain [9][10][11][12], and arbitrary dimensions [13]; diffusion in the presence of non-exponential resetting time distributions e.g., deterministic [14], intermittent [4], non-Markovian [15], non-stationary [16], with general time dependent resetting rates [17], as well as other protocols [18]; and diffusion in the presence of interactions [19][20][21]. The effect of resetting on random walks [22,23], continuous time random walks [24][25][26], Lévy flights [27,28], and other forms of stochastic motion [29][30][31][32][33], has also been studied.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent density of diffusion with stochastic resetting is invariant to return speed

2019

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The canonical Evans-Majumdar model for diffusion with stochastic resetting to the origin assumes that resetting takes zero time: upon resetting the diffusing particle is teleported back to the origin to start its motion anew. However, in reality getting from one place to another takes a finite amount of time which must be accounted for as diffusion with resetting already serves as a model for a myriad of processes in physics and beyond. Here we consider a situation where upon resetting the diffusing particle returns to the origin at a finite (rather than infinite) speed. This creates a coupling between the particle's random position at the moment of resetting and its return time, and further gives rise to a non-trivial cross-talk between two separate phases of motion: the diffusive phase and the return phase. We show that each of these phases relaxes to the stead-state in a unique manner; and while this could have also rendered the total relaxation dynamics extremely non-trivial our analysis surprisingly reveals otherwise. Indeed, the time-dependent distribution describing the particle's position in our model is completely invariant to the speed of return. Thus, whether returns are slow or fast, we always recover the result originally obtained for diffusion with instantaneous returns to the origin.

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First passage under stochastic resetting in an interval

Cited by 156 publications

References 56 publications

Péclet number governs transition to acceleratory restart in drift-diffusion

Péclet number governs transition to acceleratory restart in drift-diffusion

Stochastic resetting in underdamped Brownian motion

Time-dependent density of diffusion with stochastic resetting is invariant to return speed

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