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Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP

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.

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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.

Item Type:Article
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Ferrari, Patrik L.0000-0003-3090-5129
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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Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Subject Keywords:mathematical physics; statistical mechanics; probability
Issue or Number:2
Classification Code:MSC classes: 82C22, 60K35, 15A52
Record Number:CaltechAUTHORS:20091013-195024865
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16335
Deposited By: Joy Painter
Deposited On:14 Oct 2009 16:28
Last Modified:08 Nov 2021 23:26

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