First passages in bounded domains: When is the mean first passage time meaningful?

Mattos, Thiago Gomes de; Mejía‐Monasterio, Carlos; Metzler, Ralf; Oshanin, Gleb

doi:10.1103/physreve.86.031143

Cited by 142 publications

(154 citation statements)

References 74 publications

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“…Remarkable recent progress has been reported for first passage problems, such as the universality of certain classes of mean and global mean first passage times [30,43,44]. Moreover, it has been discussed that mean search times are not always meaningful, as they may not be representative [45,46], or that they are vastly different from the most probably first passage time obtained from the full distribution of first passage times [47,48]. However, these studies only address the problem of finding single targets.…”

Section: Introductionmentioning

confidence: 99%

Comparison of pure and combined search strategies for single and multiple targets

et al. 2017

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Abstract. We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Lévy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Lévy searcher.

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Section: Introductionmentioning

confidence: 99%

Comparison of pure and combined search strategies for single and multiple targets

et al. 2017

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“…In these settings basic goals are to maximize the probability that the target is actually found and to minimize the time and/or the cost required to find the target. In response to these challenges, a wide variety of search algorithms have been extensively investigated and rich dynamical behaviors have been uncovered [14,15].…”

Section: Introductionmentioning

confidence: 99%

Stochastic search with Poisson and deterministic resetting

Bhat¹,

Bacco²,

Redner³

2016

J. Stat. Mech.

140

136

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Abstract.We investigate a stochastic search process in one, two, and three dimensions in which N diffusing searchers that all start at x 0 seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate r, or deterministically, with a reset time T . In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large N , resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for N searchers, including the search time being independent of T for 1/T → 0 and the search cost being independent of N over a suitable range of N . Moreover, deterministic resetting typically leads to a lower search cost than in stochastic resetting.

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“…Turning finally to the limit ǫ → 0, we find that the leading small-ǫ behaviour of the moment-generating function is given by 18) for α < 2, while for α > 2 it obeys…”

Section: The Moment-generating Function For α =mentioning

confidence: 91%

“…Even in bounded systems, substantial manifestations of trajectory-totrajectory fluctuations in first passage time phenomena have been revealed [17,18]. If one is interested in determining the diffusion coefficient of a given particle, standard fitting procedures applied to finite albeit very long trajectories unavoidably lead to fluctuating estimates D f of the diffusion coefficient, which might be very different from the true ensemble average value D, defined in a standard fashion as…”

Section: Introductionmentioning

confidence: 99%

Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient

Boyer¹,

Dean²,

Mejía‐Monasterio³

et al. 2013

J. Stat. Mech.

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Abstract. In this paper we study the distribution function P (u α ) of the estimatorst dt, which optimise the least-squares fitting of the diffusion coefficient D f of a single d-dimensional Brownian trajectory B t . We pursue here the optimisation further by considering a family of weight functions of the form ω(t) = (t 0 + t) −α , where t 0 is a time lag and α is an arbitrary real number, and seeking such values of α for which the estimators most efficiently filter out the fluctuations. We calculate P (u α ) exactly for arbitrary α and arbitrary spatial dimension d, and show that only for α = 2 the distribution P (u α ) converges, as ǫ = t 0 /T → 0, to the Dirac delta-function centered at the ensemble average value of the estimator. This allows us to conclude that only the estimators with α = 2 possess an ergodic property, so that the ensemble averaged diffusion coefficient can be obtained with any necessary precision from a single trajectory data, but at the expense of a progressively higher experimental resolution. For any α = 2 the distribution attains, as ǫ → 0, a certain limiting form with a finite variance, which signifies that such estimators are not ergodic.

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First passages in bounded domains: When is the mean first passage time meaningful?

Cited by 142 publications

References 74 publications

Comparison of pure and combined search strategies for single and multiple targets

Comparison of pure and combined search strategies for single and multiple targets

Stochastic search with Poisson and deterministic resetting

Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient

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