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We consider a $q$-TASEP model started from step initial condition where all but finitely many particles have speed $1$ and a few particles are slower.
Invariant measures for the zero range process
E. D. Andjel · 1982
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Amplitude universality for driven interfaces and directed polymers in random media
J. Krug, P. Meakin, and T. Halpin-Healy · 1992
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Exact results for one-dimensional totally asymmetric diffusion models
T. Sasamoto and M. Wadati · 1998
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Shape fluctuations and random matrices
K. Johansson · 2000
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Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
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P. M. Bleher and A. B. J. Kuijlaars · 2005
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Tracy-Widom asymptotics for q q -TASEP
P. L. Ferrari and B. Veto · 2013
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Macdonald processes
A. Borodin and I. Corwin · 2014
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From duality to determinants for q-tasep and asep
A. Borodin, I. Corwin, and T. Sasamoto · 2014
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Free energy fluctuations for directed polymers in random media in 1+ 1 dimension
Alexei Borodin, Ivan Corwin, and Patrik Ferrari · 2014
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