{"title":"Integral formulas for two-layer Schur and Whittaker processes","authors":"Guillaume Barraquand","doi":"arxiv-2409.08927","DOIUrl":null,"url":null,"abstract":"Stationary measures of last passage percolation with geometric weights and\nthe log-gamma polymer in a strip of the $\\mathbb Z^2$ lattice are characterized\nin arXiv:2306.05983 using variants of Schur and Whittaker processes, called\ntwo-layer Gibbs measures. In this article, we prove contour integral formulas\ncharacterizing the multipoint joint distribution of two-layer Schur and\nWhittaker processes. We also express them as Doob transformed Markov processes\nwith explicit transition kernels. As an example of application of our formulas,\nwe compute the growth rate of the KPZ equation on $[0,L]$ with arbitrary\nboundary parameters.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08927","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.