article · 30/09/2011
Encounter distribution of two random walkers on a finite one-dimensional interval
Résumé
We analyse the first-passage properties of two random walkers confined to a finite one-dimensional domain. For the case of absorbing boundaries at the endpoints of the interval, we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries. For the case of reflecting boundaries, we obtain the mean first encounter time of the two particles. Our approach leads to closed-form expressions that are more easily tractable than a previously derived solution in terms of the Weierstrass' elliptic function.
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Tejedor, V., Schad, M., Benichou, O., Voituriez, R., & Metzler, R. (2011). Encounter distribution of two random walkers on a finite one-dimensional interval. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44(39). https://doi.org/10.1088/1751-8113/44/39/395005@article{Tejedor2011_254,
author = {Tejedor, Vincent and Schad, Michaela and Benichou, Olivier and Voituriez, Raphael and Metzler, Ralf},
year = {2011},
month = {9},
title = {Encounter distribution of two random walkers on a finite one-dimensional interval},
journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
volume = {44},
number = {39},
abstract = {We analyse the first-passage properties of two random walkers confined to a finite one-dimensional domain. For the case of absorbing boundaries at the endpoints of the interval, we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries. For the case of reflecting boundaries, we obtain the mean first encounter time of the two particles. Our approach leads to closed-form expressions that are more easily tractable than a previously derived solution in terms of the Weierstrass' elliptic function.},
url = {http://www.dx.doi.org/10.1088/1751-8113/44/39/395005},
doi = {10.1088/1751-8113/44/39/395005},
issn = {1751-8113},
}TY - JOUR
AU - Tejedor, Vincent
AU - Schad, Michaela
AU - Benichou, Olivier
AU - Voituriez, Raphael
AU - Metzler, Ralf
PY - 2011
DA - 2011/09/30
TI - Encounter distribution of two random walkers on a finite one-dimensional interval
JO - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
VL - 44
IS - 39
SN - 1751-8113
AB - We analyse the first-passage properties of two random walkers confined to a finite one-dimensional domain. For the case of absorbing boundaries at the endpoints of the interval, we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries. For the case of reflecting boundaries, we obtain the mean first encounter time of the two particles. Our approach leads to closed-form expressions that are more easily tractable than a previously derived solution in terms of the Weierstrass' elliptic function.
DO - 10.1088/1751-8113/44/39/395005
UR - http://www.dx.doi.org/10.1088/1751-8113/44/39/395005
ER -