Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition

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dc.creatorImamura, T.
dc.creatorSasamoto, T.
dc.date2007-02-02
dc.date2007-07-06
dc.date.accessioned2026-07-07T08:23:58Z
dc.date.available2026-07-07T08:23:58Z
dc.descriptionThe one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.
dc.description48 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0702009
dc.identifierhttp://arxiv.org/abs/math-ph/0702009
dc.identifierJ. Stat. Phys. 128 (2007) 799-846
dc.identifierdoi:10.1007/s10955-007-9326-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136190
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.subjectExactly Solvable and Integrable Systems
dc.titleDynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
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