Borodin, Alexei and Ferrari, Patrik L. and Sasamoto, Tomohiro (2008) Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP. Communications in Mathematical Physics, 283 (2). pp. 417-449. ISSN 0010-3616. doi:10.1007/s00220-008-0515-4. https://resolver.caltech.edu/CaltechAUTHORS:20091013-195024865
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Abstract
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy_1 process. This result holds more generally for the observation points located along any space-like path in the space-time plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update.
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Additional Information: | © 2008 Springer. Received: 13 August 2007 Accepted: 20 December 2007 Published online: 29 May 2008. A. Borodin was partially supported by the NSF grants DMS-0402047 and DMS-0707163. P.L. Ferrari is grateful to H. Spohn for useful discussions. 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. | ||||||||||||
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Subject Keywords: | mathematical physics; statistical mechanics; probability | ||||||||||||
Issue or Number: | 2 | ||||||||||||
Classification Code: | MSC classes: 82C22, 60K35, 15A52 | ||||||||||||
DOI: | 10.1007/s00220-008-0515-4 | ||||||||||||
Record Number: | CaltechAUTHORS:20091013-195024865 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20091013-195024865 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 16335 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Joy Painter | ||||||||||||
Deposited On: | 14 Oct 2009 16:28 | ||||||||||||
Last Modified: | 08 Nov 2021 23:26 |
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