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arXiv 2601.130862026-01-19math.PRmath.GTmath.SP

布朗运动环与Selberg泽塔函数

Brownian Loops and the Selberg Zeta Function

Eidgenössische Technische Hochschule Zürich（苏黎世联邦理工学院）；Institut des Hautes Études Scientifiques（高等科学研究所）

Roman Lemonde, Jian Wang

备注：: 19 pages, 1 figure

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AI总结：

本文研究了双曲面上布朗环测度与Selberg泽塔函数的关系，并提供了正则化拉普拉斯算子确定性的概率解释。

摘要：

我们研究了在双曲面上具有恒定杀灭率的布朗运动的布朗环测度。我们计算了在自由同源类中具有杀灭的布朗环的质量，然后当表面几何有限时，将所有本质同源类中环的总质量与Selberg泽塔函数联系起来。作为应用，我们提供了不同正则化拉普拉斯算子确定性的概率解释，包括紧致和无限面积情况。

英文摘要：

We study the Brownian loop measure on hyperbolic surfaces for Brownian motion with a constant killing rate. We compute the mass of Brownian loops with killing in a free homotopy class and then relate the total mass of loops in all essential homotopy classes to the Selberg zeta function when the surface is geometrically finite. As an application, we provide a probabilistic interpretation of different notions of regularized determinants of Laplacian, in both the compact and infinite-area cases.

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