发表机构
Université Paris Cité; ESPCI Paris, Université PSL（巴黎西岱大学; 巴黎高等物理化工学院，巴黎文理研究大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究揭示Langevin动力学中的自谐波漂移与随机局域化的联系，指出紧致化源于自治漂移要求，可能扩展随机局域化的应用范围。
AI 中文摘要
我们近期关于具有自谐波漂移和经典自旋的Langevin动力学的研究，揭示了其与“随机局域化”（Stochastic Localization）之间的紧密联系，后者是数学几何和数据科学领域备受关注的概念。粗略地说，前者可视为后者的一种版本，其中$n$维欧几里得空间——即后者中出现的概率分布函数的定义域——被“紧致化”为$n$维球面。通过比较这两个框架，我们认为这种紧致化是要求漂移为自治（autonomous）的结果。这两种方法之间的关系可能扩展随机局域化的应用范围。
英文摘要
Our recent research on Langevin dynamics with self-harmonic drift and classical spins has revealed a strong connection to ``Stochastic Localization," a concept attracting attention in the fields of mathematical geometry and data science. Roughly speaking, the former can be viewed as a version of the latter in which the $n$-dimensional Euclidean space - the domain of the probability distribution function appearing in the latter - is ``compactified'' to the surface of an $n$-dimensional sphere. By comparing the two frameworks, we argue that this compactification is a consequence of requiring the drift to be autonomous. The relationship between the two approaches may expand the scope of Stochastic Localization.
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