Scholarlink

<p>We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schrödinger-type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant yields the ubiquitous Tracy–Widom distribution Tracy and Widom (Commun Math Phys 159(1610):151–174, (1994). https://doi.org/10.1007/BF02100489 , which has found many applications in numerous domains. In this paper, we unveil a generalization of the Tracy–Widom distribution for a generic class of defining functions. Furthermore, we bring forth a direct application of our upshot and survey the relation between the framework which we employ and isomonodromic systems.</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

Fredholm determinants from Schrödinger-type equations, and deformation of Tracy–Widom distribution

  • 期刊论文

  • 发表日期：

    2026年2月2日

查看全文
  • Taro Kimura,
  • Xavier Navand

摘要

We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schrödinger-type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant yields the ubiquitous Tracy–Widom distribution Tracy and Widom (Commun Math Phys 159(1610):151–174, (1994). https://doi.org/10.1007/BF02100489 , which has found many applications in numerous domains. In this paper, we unveil a generalization of the Tracy–Widom distribution for a generic class of defining functions. Furthermore, we bring forth a direct application of our upshot and survey the relation between the framework which we employ and isomonodromic systems.