An explicit formula of the limit of the heat kernel measures on the spheres embedded in R^∞

Minh Luan Doan; Evan M. O’Dorney

doi:10.48550/arxiv.2510.25855

October 29, 2025Open Access

An explicit formula of the limit of the heat kernel measures on the spheres embedded in R^∞

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Key Points

The heat kernel measures converge to a Gaussian measure in R^infinity, with implications for geometric analysis.
The explicit formula elucidates the relationship between heat kernel measures and Gaussian measures.
Spheres embedded in infinite-dimensional space were analyzed, showing their mathematical properties and limits.
This convergence may enhance understanding of geometric structures and their measures in infinite dimensions.

Implication

Analysis reveals heat kernel measures converge to Gaussian measure at the north pole of spheres, indicating significant geometric implications.

Abstract

We show that the heat kernel measures based at the north pole of the spheres SN-1(√ N), with properly scaled radius √ N and adjusted center, converge to a Gaussian measure in R^∞, and find an explicit formula for this measure.

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Cite This Study

Doan et al. (2025) studied this question.

synapsesocial.com/papers/690fdcdaf60c54d04ea37fbc https://doi.org/10.48550/arxiv.2510.25855

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An explicit formula of the limit of the heat kernel measures on the spheres embedded in R^∞

Key Points

Implication

Abstract

Discussion

Cite This Study

An explicit formula of the limit of the heat kernel measures on the spheres embedded in R^∞

Key Points

Implication

Abstract

Discussion

Cite This Study

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