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.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 198, No. 1, pp. 79–100, January, 2019.
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Imamura, T., Sasamoto, T. The q-TASEP with a Random Initial Condition. Theor Math Phys 198, 69–88 (2019). https://doi.org/10.1134/S0040577919010057
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DOI: https://doi.org/10.1134/S0040577919010057