Extreme economic outcomes are not shaped by tails alone. They are also shaped by unequal access to opportunities. This paper develops a theory of heterogeneous extremes by taking the distribution of opportunity access as the object of study. In a mixed Poisson search setting, normalized maxima admit a Laplace mixture representation that yields order comparisons and a clean benchmark against the homogeneous economy. The main contribution is geometric: a canonical coupling turns differences in heterogeneity into optimal transport bounds for the whole induced law of extremes, the full schedule of top quantiles, and structured counterfactual paths between economies. The paper also derives a second order expansion that separates classical extreme value approximation error from heterogeneity effects. As a complementary normative exercise, it studies an entropy regularized design problem for reallocating opportunities under a mean constraint. A stylized labor market network application interprets heterogeneity as unequal access to job opportunities and shows how the framework can be used for tail counterfactuals and robustness analysis of top wage distributions.

翻译：极端经济结果并非仅由尾部分布塑造，机会获取的不平等同样起着关键作用。本文以机会获取分布为研究对象，提出了一套异质极端事件理论。在混合泊松搜索环境中，标准化极大值具有Laplace混合表示，这一表示可导出顺序比较结果，并建立与同质经济体的清晰基准对照。本文的主要贡献在于几何层面：通过规范耦合将异质性差异转化为针对极端事件诱导全律、顶级分位数完整序列及经济体间结构化反事实路径的最优传输界。此外，本文推导了将经典极值逼近误差与异质性效应分离的二阶展开式。作为补充性规范分析，本文研究了均值约束下机会再分配的熵正则化设计问题。通过一个简化的劳动力市场网络应用，将异质性诠释为获取工作机会的不平等性，并展示该框架如何用于尾部反事实分析及顶层工资分布的稳健性检验。