重正化群作为随机探索过程
The Renormalization Group as a Stochastic Exploration Process
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中文总结 AI 辅助
该研究将重正化群（RG）重新诠释为探索物理相空间的随机过程，建立了其与施拉姆-洛厄纳演化等随机过程的联系，关联了RG概念与概率工具及随机量子化。
中文摘要 AI 辅助
重正化群（RG）是分析复杂物理系统的强大通用框架。本文将其重新诠释为一种随机过程，它按尺度探索物理相空间，逐步揭示小尺度结构的更精细细节。该视角建立了它与其他随机探索过程（如施拉姆-洛厄纳演化）的自然联系，更适合概率学受众。它将RG变换、有效作用量等RG概念与条件期望、鞅等常用概率工具关联，也与随机量子化建立了联系。
英文摘要
The Renormalization Group (RG) is a powerful and versatile framework for analyzing complex physical systems. Here, we reinterpret it as a stochastic process that explores physical phase spaces, scale by scale, progressively revealing finer details of small-scale structures. This perspective establishes a natural connection to other random exploration processes, such as the Schramm-Loewner evolution, and is more suited for a probabilist audience. It links RG concepts such as RG transformations, effective actions, etc, to usual probabilistic tools such as conditional expectation values, martingales, etc, but also makes contact with stochastic quantization.
