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Integral formulas for two-layer Schur and Whittaker processes
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abstract
Stationary measures of last passage percolation with geometric weights and the log-gamma polymer in a strip of the $\mathbb Z^2$ lattice are characterized in arXiv:2306.05983 using variants of Schur and Whittaker processes, called two-layer Gibbs measures. In this article, we prove contour integral formulas characterizing the multipoint joint distribution of two-layer Schur and Whittaker processes. We also express them as Doob transformed Markov processes with explicit transition kernels. As an example of application of our formulas, we compute the growth rate of the KPZ equation on $[0,L]$ with arbitrary boundary parameters.
Forward citations
Cited by 2 Pith papers
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Stationary measures for log-gamma polymer on a strip and in half-space
The strip stationary measure has three phases plus a coexistence line, and converges to the half-space stationary measure with drift min{0,u,v}.
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Free Askey--Wilson functionals and geometric last passage percolation on a strip
Free Askey-Wilson functionals yield generating function representations for geometric LPP on a strip, giving the full phase diagram of the stationary measure and a Poisson approximation.
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