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Fluctuation Properties of the TASEP with Periodic Initial Configuration

Borodin, Alexei and Ferrari, Patrik L. and Prähofer, Michael and Sasamoto, Tomohiro (2007) Fluctuation Properties of the TASEP with Periodic Initial Configuration. Journal of Statistical Physics, 129 (5-6). pp. 1055-1080. ISSN 0022-4715. doi:10.1007/s10955-007-9383-0. https://resolver.caltech.edu/CaltechAUTHORS:20191015-100453408

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Abstract

We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us (Sasamoto in J. Phys. A 38:L549–L556, 2005) and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s10955-007-9383-0DOIArticle
https://rdcu.be/bUl4NPublisherFree ReadCube access
https://arxiv.org/abs/math-ph/0608056arXivDiscussion Paper
ORCID:
AuthorORCID
Ferrari, Patrik L.0000-0003-3090-5129
Prähofer, Michael0000-0002-5289-7898
Additional Information:© 2007 Springer Science+Business Media, LLC. Received: 14 December 2006; Accepted: 24 July 2007; Published online: 6 October 2007. P.L. Ferrari would like to thank H. Spohn for useful discussions and for suggesting the compact form of the kernel obtained during our previous work [11]. A. Borodin was partially supported by the NSF grant DMS-0402047 and the CRDF grant RIM1-2622-ST-04. The work of T. Sasamoto is partly supported by the Grant-in-Aid for Young Scientists (B), the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Funders:
Funding AgencyGrant Number
NSFDMS-0402047
Civilian Research & Development FoundationRIM1-2622-ST-04
Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Subject Keywords:Random Matrice; Stat Phys; Fredholm Determinant; Totally Asymmetric Simple Exclusion Process; Asymmetric Simple Exclusion Process
Issue or Number:5-6
DOI:10.1007/s10955-007-9383-0
Record Number:CaltechAUTHORS:20191015-100453408
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191015-100453408
Official Citation:Borodin, A., Ferrari, P.L., Prähofer, M. et al. J Stat Phys (2007) 129: 1055. https://doi.org/10.1007/s10955-007-9383-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99268
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Oct 2019 17:34
Last Modified:16 Nov 2021 17:45

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