Mean first-passage times in confined media: from Markovian to non-Markovian processes
| hal.structure.identifier | Laboratoire de Physique Théorique de la Matière Condensée [LPTMC] | |
| dc.contributor.author | BENICHOU, Olivier | |
| hal.structure.identifier | Laboratoire Ondes et Matière d'Aquitaine [LOMA] | |
| dc.contributor.author | GUÉRIN, Thomas | |
| hal.structure.identifier | Laboratoire de Physique Théorique de la Matière Condensée [LPTMC] | |
| dc.contributor.author | VOITURIEZ, Raphaël | |
| dc.date.issued | 2015-04-02 | |
| dc.identifier.issn | 1751-8113 | |
| dc.description.abstractEn | We review recent theoretical works that enable the accurate evaluation of the mean first passage time (MFPT) of a random walker to a target in confinement for Markovian (memory-less) and non-Markovian walkers. For the Markovian problem, we present a general theory which allows one to accurately evaluate the MFPT and its extensions to related first-passage observables such as splitting probabilities and occupation times. We show that this analytical approach provides a universal scaling dependence of the MFPT on both the volume of the confining domain and the source target distance in the case of general scale-invariant processes. This analysis is applicable to a broad range of stochastic processes characterized by length scale-invariant properties, and reveals the key role that can be played by the starting position of the random walker. We then present an extension to non-Markovian walks by taking the specific example of a tagged monomer of a polymer chain looking for a target in confinement. We show that the MFPT can be calculated accurately by computing the distribution of the positions of all the monomers in the chain at the instant of reaction. Such a theory can be used to derive asymptotic relations that generalize the scaling dependence with the volume and the initial distance to the target derived for Markovian walks. Finally, we present an application of this theory to the problem of the first contact time between the two ends of a polymer chain, and review the various theoretical approaches of this non-Markovian problem. | |
| dc.language.iso | en | |
| dc.publisher | IOP Publishing | |
| dc.subject.en | Random Walks | |
| dc.subject.en | First-passage times | |
| dc.subject.en | Stochastic Processes | |
| dc.title.en | Mean first-passage times in confined media: from Markovian to non-Markovian processes | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1088/1751-8113/48/16/163001 | |
| dc.subject.hal | Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech] | |
| dc.description.sponsorshipEurope | First-passage times and optimization of target search strategies | |
| bordeaux.journal | Journal of Physics A: Mathematical and Theoretical | |
| bordeaux.page | 1630001 (1-43) | |
| bordeaux.volume | 48 | |
| bordeaux.issue | 16 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01146165 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01146165v1 | |
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