On the $q$-TASEP with a random initial condition

Abstract

When studying fluctuations of models in the 1D KPZ class including the ASEP and the $q$-TASEP, a standard approach has been to first write down a formula for $q$-deformed moments and constitute their generating function. This works well for the step initial condition, but there is a difficulty for a random initial condition (including the stationary case): in this case only the first few moments are finite and the rest diverge. In a previous work [16], we presented a method dealing directly with the $q$-deformed Laplace transform of an observable, in which the above difficulty does not appear. There the Ramanujan's summation formula and the Cauchy determinant for the theta functions play an important role. In this note, we give an alternative approach for the $q$-TASEP without using them.

20 pages

References in corpus (6)

• Fluctuation properties of the TASEP with periodic initial configuration
• The one-dimensional KPZ equation and its universality class
• Fluctuations of the one-dimensional polynuclear growth model with external sources
• Current Fluctuations of the Stationary ASEP and Six-Vertex Model
• The ASEP and determinantal point processes
• Lectures on Integrable probability: Stochastic vertex models and symmetric functions