# Spectral Gaps for Reversible Markov Processes with Chaotic Invariant Measures: The Kac Process with Hard Sphere Collisions in Three Dimensions

## TL;DR

This paper introduces a new method to estimate spectral gaps in reversible Markov processes with chaotic measures, successfully proving the Kac conjecture for 3D hard sphere collisions.

## Contribution

It presents a novel approach for spectral gap estimation and applies it to resolve the long-standing Kac conjecture in three-dimensional hard sphere models.

## Key findings

- Spectral gap estimates for the Kac process in 3D
- Proof of the Kac conjecture for hard sphere collisions
- Development of a new method for spectral gap analysis

## Abstract

We develop a method for producing estimates on the spectral gaps of reversible Markov jump processes with chaotic invariant measures, and we apply it to prove the Kac conjecture for hard sphere collision in three dimensions.