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.
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| 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. | ||||||||||||
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| 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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