Published November 2008
| Version Submitted
Journal Article
Open
Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
-
1.
California Institute of Technology
-
2.
Weierstrass Institute for Applied Analysis and Stochastics
-
3.
Chiba University
Abstract
We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions, starting with certain deterministic initial conditions. For large time t, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy_1 and Airy_2 processes, whose one‐point distributions are the GOE and GUE Tracy‐Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one‐point distribution is a new interpolation between GOE and GUE edge distributions
Additional Information
© 2007 Wiley Periodicals, Inc. Issue Online: 22 August 2008; Version of Record online: 28 December 2007; Manuscript received: 01 March 2007. A. Borodin was partially supported by the NSF grant DMS-0402047 and the CRDF grant RIM1-2622-ST-04. P.L. Ferrari would like to thank for the support of the German-Japanese cooperation project of German National Foundation, DFG 446JAP113/325/0-1. The work of T. Sasamoto is supported by the Grant-in-Aid for Young Scientists (B), the Ministry of Education, Culture, Sports, Science and Technology, Japan.Attached Files
Submitted - 0703023.pdf
Files
0703023.pdf
Additional details
Additional titles
- Alternative title
- Transition between Airy1 and Airy2 processes and TASEP fluctuations
Identifiers
- Eprint ID
- 89922
- Resolver ID
- CaltechAUTHORS:20180925-133041457
Related works
- Describes
- https://arxiv.org/abs/math-ph/0703023 (URL)
Funding
- NSF
- DMS-0402047
- Civilian Research & Development Foundation
- RIM1-2622-ST-04
- Deutsche Forschungsgemeinschaft (DFG)
- 446JAP113/325/0-1
- Ministry of Education, Culture, Sports, Science and Technology (MEXT)
Dates
- Created
-
2018-09-25Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field