Scholarlink

Consider a p-dimensional beta-type simplex in \(\mathbb {R}^d\) . In this chapter, we prove limit theorems for the distribution of its log-volume and volume in high dimensions, that is, in the asymptotic regime where \(d\to \infty \) and where we allow \(p=p(d)\) to depend on d. Our approach is based on proving mod-Gaussian convergence of the log-volume, which in turn relies on a detailed asymptotic analysis of the explicit formula for the moments of the volume, as stated in Theorem 6.13 .

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

Limit Theorems for Volumes of Beta-Type Simplices

  • 章节

  • 发表日期：

    2026年

查看全文
  • Zakhar Kabluchko,
  • David Albert Steigenberger,
  • Christoph Thäle

摘要

Consider a p-dimensional beta-type simplex in \(\mathbb {R}^d\) . In this chapter, we prove limit theorems for the distribution of its log-volume and volume in high dimensions, that is, in the asymptotic regime where \(d\to \infty \) and where we allow \(p=p(d)\) to depend on d. Our approach is based on proving mod-Gaussian convergence of the log-volume, which in turn relies on a detailed asymptotic analysis of the explicit formula for the moments of the volume, as stated in Theorem 6.13 .