Communications in Mathematical Physics

, Volume 290, Issue 1, pp 129–154 | Cite as

Asymptotics in ASEP with Step Initial Condition

  • Craig A. Tracy
  • Harold WidomEmail author
Open Access


In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three asymptotic results for the positions of these particles. In one an apparently new distribution function arises and in another the distribution function F 2 arises. The latter extends a result of Johansson on TASEP to ASEP, and hence proves KPZ universality for ASEP with step initial condition.


Saddle Point Closed Curf Trace Norm Integer Lattice Fredholm Determinant 
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This work was supported by the National Science Foundation through grants DMS-0553379 (first author) and DMS-0552388 (second author).

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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