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Asymptotic exponential moments of two-dimensional additiv...
[Submitted on 30 Apr 2025 (v1), last revised 3 Aug 2026 (this ve · 2025-05-01 · via math updates on arXiv.org

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Abstract:We introduce new asymptotic formulas for the exponential moments of rescaled additive functionals of two-dimensional Brownian motion, extending the analysis to parameter regimes that go beyond the subcritical case underlying distributional limits. As an application, we develop a probabilistic-analytic approximation for the two-dimensional Laplacian with a singular perturbation at the origin. This method describes the perturbed Laplacian by combining analytic characteristics of the Kallianpur-Robbins and Kasahara-Kotani laws.

Submission history

From: Yu-Ting Chen [view email]
[v1] Wed, 30 Apr 2025 16:52:58 UTC (43 KB)
[v2] Fri, 16 May 2025 18:40:26 UTC (43 KB)
[v3] Mon, 3 Aug 2026 18:18:40 UTC (50 KB)