# Gaussian Limit for High-Dimensional Spherical Means

## TL;DR

This paper proves that integrals over high-dimensional spherical slices converge to Gaussian integrals in an infinite-dimensional setting, revealing a fundamental limit behavior in high-dimensional geometry.

## Contribution

It establishes a new Gaussian limit theorem for spherical means in high dimensions, extending classical results to infinite-dimensional spaces.

## Key findings

- High-dimensional spherical integrals tend to Gaussian integrals.
- The limit holds in an infinite-dimensional affine subspace.
- Provides a rigorous mathematical foundation for high-dimensional spherical analysis.

## Abstract

We show that 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.