Lower bound for the escape probability in the Lorentz Mirror Model on the lattice

TL;DR

This paper establishes a lower bound on the probability that a particle in the Lorentz mirror model reaches a certain distance, regardless of mirror density, highlighting a fundamental property of the model's behavior.

Contribution

The paper proves a universal lower bound for escape probability in the Lorentz mirror model on the lattice, independent of mirror density.

Findings

Probability of reaching distance n is at least 1/(2n+1)

Lower bound holds for any mirror density

Results provide insight into particle escape dynamics

Abstract

We show that in the Lorentz mirror model, at any density of mirrors, the probability of a particle starting at the origin to reach distance n is at least 1/(2n+1).