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

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.