Geodesic
The~$q$-TASEP with a~random initial condition
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 79-100

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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.
Mots-clés : exclusion process, fluctuation
Keywords: $q$-Whittaker function, random matrix theory. 
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     author = {T. Imamura and T. Sasamoto},
     title = {The~$q${-TASEP} with a~random initial condition},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {79--100},
     publisher = {mathdoc},
     volume = {198},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a4/}
}
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T. Imamura; T. Sasamoto. The~$q$-TASEP with a~random initial condition. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 79-100. http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a4/