# Limiting Means for Spherical Slices

## TL;DR

This paper demonstrates that for certain functions, integrals over slices of high-dimensional spheres converge to Gaussian integrals in infinite-dimensional spaces, revealing a connection between finite and infinite-dimensional analysis.

## Contribution

It establishes a new limit theorem linking spherical slice integrals to Gaussian measures in infinite-dimensional settings.

## Key findings

- Spherical slice integrals converge to Gaussian integrals in infinite dimensions.
- The result applies to a suitable class of functions of finitely-many variables.
- Provides a bridge between finite-dimensional spherical analysis and infinite-dimensional Gaussian measures.

## Abstract

We show that for a suitable class of functions of finitely-many variables, the limit of integrals along slices of a high dimensional sphere is a Gaussian integral on a corresponding finite-codimension affine subspace in infinite dimensions.