Scholarlink

<p>We consider the <i>n</i>-point, fixed-time large deviations of the KPZ equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations and a wide range of scaling regimes that allows time to be short, unit-order, and long. We prove the <i>n</i>-point large deviation principle and characterize, with proof, the corresponding spacetime limit shape. Our proof is based on the results—from the companion paper (Tsai in High moments of the SHE in the clustering regimes, 2023)—on moments of the stochastic heat equation and utilizes ideas coming from a tree decomposition. Behind our proof lies the phenomenon where the major contribution of the noise concentrates around certain corridors in spacetime, and we explicitly describe the corridors.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Spacetime Limit Shapes of the KPZ Equation in the Upper Tails

  • 期刊论文

  • 发表日期：

    2025年4月21日

查看全文
  • Yier Lin,
  • Li-Cheng Tsai

摘要

We consider the n-point, fixed-time large deviations of the KPZ equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations and a wide range of scaling regimes that allows time to be short, unit-order, and long. We prove the n-point large deviation principle and characterize, with proof, the corresponding spacetime limit shape. Our proof is based on the results—from the companion paper (Tsai in High moments of the SHE in the clustering regimes, 2023)—on moments of the stochastic heat equation and utilizes ideas coming from a tree decomposition. Behind our proof lies the phenomenon where the major contribution of the noise concentrates around certain corridors in spacetime, and we explicitly describe the corridors.