Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion

Tejedor, Vincent; Bénichou, Olivier; Metzler, Ralf; Voituriez, Raphaël

doi:10.1088/1751-8113/44/25/255003

Cited by 14 publications

(17 citation statements)

References 29 publications

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“…It may be mentioned here that the first passage time in complex scale invariant media was studied [13]. The thoery of mean first passage time for jump processes are developed [14] and verified by applying in Levy flights and fractional Brownian motion. The statistics of the gap and time interval between the highest positions of a Markovian one dimensional random walker [15], the universal statistics of longest lasting records of random walks and Levy flights are also studied [16].…”

Section: Introductionmentioning

confidence: 90%

Model and Statistical Analysis of the Motion of a Tired Random Walker in Continuum

Acharyya¹

2015

JMP

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The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional continuum. In all cases, the diffusive nature of walker, breaks down due to tiring which is quite obvious. In one dimension, the distribution of the displacement of a tired walker remains Gaussian (as observed in normal walker) with reduced width. In two and three dimensions, the probability distribution of displacement becomes nonmonotonic and unimodal. The most probable displacement and the deviation reduces as the tiring factor increases. The probability of return of a tired walker, decreases as the tiring factor increases in one and two dimensions. However, in three dimensions, it is found that the probability of return almost insensitive to the tiring factor. The probability distributions of first return time of a tired random walker do not show the scale invariance as observed for a normal walker in continuum. The exponents, of such power law distributions of first return time, in all three dimensions are estimated for normal walker. The exit probability and the probability distribution of first passage time are found in all three dimensions. A few results are compared with available analytical calculations for normal walker.

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Section: Introductionmentioning

confidence: 90%

Model and Statistical Analysis of the Motion of a Tired Random Walker in Continuum

Acharyya¹

2015

JMP

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“…In a recent review article of first passage problems in finite domains [33], it is remarked that although problems involving stationary traps have been well-studied, the case of mobile traps still remains largely unexplored. In particular, the only studies to have considered mobile traps in confined geometries have done so in one dimension [34,35,36,37]. Mobile traps are not only more realistic in many applications, but can significantly increase or decrease MFPT depending on parameters of their motion.…”

Section: Introductionmentioning

confidence: 99%

Mean First Passage Time for a Small Rotating Trap inside a Reflective Disk

Tzou

Kolokolnikov

2015

Multiscale Model. Simul.

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We compute the mean first passage time (MFPT) for a Brownian particle inside a two-dimensional disk with reflective boundaries and a small interior trap that is rotating at a constant angular velocity. The inherent symmetry of the problem allows for a detailed analytic study of the situation. For a given angular velocity, we determine the optimal radius of rotation that minimizes the average MFPT over the disk. Several distinct regimes are observed, depending on the ratio between the angular velocity ω and the trap size ε, and several intricate transitions are analyzed using the tools of asymptotic analysis and Fourier series. For ω ∼ O(1), we compute a critical value ωc > 0 such that the optimal trap location is at the origin whenever ω < ωc, and is off the origin for ω > ωc. In the regime 1 ω O(ε −1 ) the optimal trap path approaches the boundary of the disk. However as ω is further increased to O(ε −1 ), the optimal trap path "jumps" closer to the origin. Finally for ω O(ε −1 ) the optimal trap path subdivides the disk into two regions of equal area. This simple geometry provides a good test case for future studies of MFPT with more complex trap motion.

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“…Hence, in Eq. ( 11), T 0 /D is the search time expected for a non persistent random searcher of same normalized diffusion coefficient D. Note that the persistence property yields a non trivial additive correction which scales linearly with the volume, and therefore should not be neglected; this could be related to the "residual" mean first passage time described in [26]. As shown in Fig.…”

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confidence: 99%

Optimizing Persistent Random Searches

2012

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We consider a minimal model of persistent random searcher with a short range memory. We calculate exactly for such a searcher the mean first-passage time to a target in a bounded domain and find that it admits a nontrivial minimum as function of the persistence length. This reveals an optimal search strategy which differs markedly from the simple ballistic motion obtained in the case of Poisson distributed targets. Our results show that the distribution of targets plays a crucial role in the random search problem. In particular, in the biologically relevant cases of either a single target or regular patterns of targets, we find that, in strong contrast to repeated statements in the literature, persistent random walks with exponential distribution of excursion lengths can minimize the search time, and in that sense perform better than any Levy walk.

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Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion

Cited by 14 publications

References 29 publications

Model and Statistical Analysis of the Motion of a Tired Random Walker in Continuum

Model and Statistical Analysis of the Motion of a Tired Random Walker in Continuum

Mean First Passage Time for a Small Rotating Trap inside a Reflective Disk

Optimizing Persistent Random Searches

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