Stationary measure for the open KPZ equation
Stationary measure for the open KPZ equation
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DOI：
10.1002/cpa.22174
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发表时间：
2021-03
影响因子：
3
通讯作者：
Ivan Corwin;Alisa Knizel
中科院分区：
文献类型：
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作者：
Ivan Corwin;Alisa Knizel
我们给出了空间区间[0，1]上开KPZ方程的第一个定常测度的构造，其中一般非齐次Neumann边界条件在0和1处分别依赖于真实的参数u和v.当u+v≥ 0 $u +v\ge 0$时，通过多点拉普拉斯变换，我们唯一地刻画了所构造的平稳测度，并证明了它是由一个随机过程给出的，我们称之为连续对偶Hahn过程.我们的工作依赖于开放ASEP平稳测度的Bryc和WesoWesoWrosowski的Askey-Wilson过程公式的渐近分析（这反过来又源于内山，Sasamoto和Wadati的Askey-Wilson Jacobi矩阵表示Derrida等人。的矩阵积拟法）结合Corwin和Shen的证明，即在弱不对称缩放下，开放ASEP收敛于开放KPZ。
We provide the first construction of stationary measures for the open KPZ equation on the spatial interval [0,1] with general inhomogeneous Neumann boundary conditions at 0 and 1 depending on real parameters u and v, respectively. When u+v≥0$u+v\ge 0$ , we uniquely characterize the constructed stationary measures through their multipoint Laplace transform, which we prove is given in terms of a stochastic process that we call the continuous dual Hahn process. Our work relies on asymptotic analysis of Bryc and Wesołowski's Askey–Wilson process formulas for the open ASEP stationary measure (which in turn arise from Uchiyama, Sasamoto and Wadati's Askey‐Wilson Jacobi matrix representation of Derrida et al.'s matrix product ansatz) in conjunction with Corwin and Shen's proof that open ASEP converges to open KPZ under weakly asymmetric scaling.