重新审视英格尔顿不等式的稳定性：一种无热带化方法
Revisiting the Stability of the Ingleton Inequality: A Tropicalization-Free Approach
AI总结：
研究英格尔顿不等式稳定性，用无热带化方法重新审视，开发替代框架简化概念与证明、导出误差项并改进估计，还解决了先前工作的开放问题，给出新无限熵不等式族确定两英格尔顿表达式之和的稳定性。
AI中文摘要：
经典的英格尔顿不等式在特定精确条件独立约束下对熵点成立。Matveev和Romashchenko（2026）研究了这些蕴含关系的稳定性，量化了一组条件互信息项小但非零时英格尔顿不等式被违反的程度。他们的证明基本依赖热带概率空间的复杂框架，本文用无热带化方法重新审视。通过开发替代框架，简化了基本概念和证明，导出显式误差项并改进估计。还解决了先前工作中的一个开放问题，展示了一个新的无限熵不等式族来确定两个英格尔顿表达式之和的稳定性。
英文摘要：
The classical Ingleton inequality is known to hold for entropic points under specific exact conditional independence constraints. Recently, Matveev and Romashchenko (2026) investigated the stability of these implications, quantifying the extent to which the Ingleton inequality can be violated when a group of conditional mutual information terms is small but non-zero. While their proofs relied fundamentally on the complex framework of tropical probability spaces, we revisit these stability results using a completely tropicalization-free approach. By developing an alternative framework, we significantly streamline the underlying concepts and proofs, derive explicit error terms, and improve some estimates. Furthermore, we resolve an open problem posed in prior work by exhibiting a new infinite family of entropy inequalities that establishes the stability of the sum of two Ingleton expressions.
