Scholarlink

<p>This paper investigates Markov-invariant geometric structures on the denormalized state space, the space of strictly positive measures on a finite set. Within the subclass of structures compatible with the classical Nagaoka–Amari structure, we characterize all flat structures on the denormalized state space and identify a distinct one that complements the classical Nagaoka–Amari structure. This companion flat structure sheds new light on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha =\pm 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <mo>±</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> symmetry of the probability simplex and is conformally related to the Nagaoka–Amari structure, providing a coherent framework for understanding their relationship.</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

A companion to the Nagaoka–Amari structure on the denormalized state space

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月14日

查看全文
  • Yoshitaka Fujiwara

摘要

This paper investigates Markov-invariant geometric structures on the denormalized state space, the space of strictly positive measures on a finite set. Within the subclass of structures compatible with the classical Nagaoka–Amari structure, we characterize all flat structures on the denormalized state space and identify a distinct one that complements the classical Nagaoka–Amari structure. This companion flat structure sheds new light on the \(\alpha =\pm 1\) α = ± 1 symmetry of the probability simplex and is conformally related to the Nagaoka–Amari structure, providing a coherent framework for understanding their relationship.