An explicit formula of the limit of the heat kernel measures on the spheres embedded in $\mathbb {R}^\infty$

Minh-Luan Doan; Evan O'Dorney

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arXiv · 2510.25855

An explicit formula of the limit of the heat kernel measures on the spheres embedded in $\mathbb {R}^\infty$

Minh-Luan Doan·Evan O'Dorney

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Abstract

We show that the heat kernel measures based at the north pole of the spheres $S^{N-1}(\sqrt N)$, with properly scaled radius $\sqrt N$ and adjusted center, converge to a Gaussian measure in $\mathbb R^\infty$, and find an explicit formula for this measure.

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Minh-Luan Doan, Evan O'Dorney. 2025-10-29. An explicit formula of the limit of the heat kernel measures on the spheres embedded in $\mathbb {R}^\infty$. https://arxiv.org/abs/2510.25855

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