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Theoretical and Mathematical Physics

, Volume 198, Issue 1, pp 69–88 | Cite as

The q-TASEP with a Random Initial Condition

  • T. ImamuraEmail author
  • T. SasamotoEmail author
Article
  • 5 Downloads

Abstract

A standard approach for studying fluctuations of one-dimensional Kardar–Parisi–Zhang models, which include the ASEP and the q-TASEP, is to write a formula for the q-deformed moments and construct their generating function. This approach works well for an initial condition of the step type but not for a random initial condition (including the stationary case): in this case, only the first few moments are finite and the rest diverge. We previously presented a method for overcoming this difficulty using the Ramanujan summation formula and the Cauchy determinant for the theta functions. Here, we present an alternative approach for the q-TASEP without using these relations.

Keywords

exclusion process fluctuation q-Whittaker function random matrix theory 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsChiba UniversityChibaJapan
  2. 2.Department of PhysicsTokyo Institute of TechnologyTokyoJapan

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