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

2013/11/28 by Gady Kozma, Kozma, Gady, Vladas Sidoravičius +2 · 1 citation
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1311.7437

2 pages. Really, just 2 pages

arxiv created 2013/11/28 · openalex publication_date 2013/11/28 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Cited by

• Hierarchical Lorentz Mirror Model: Normal Transport and a Universal 2/3 Mean--Variance Law

Related

• Polynomial bound for the localization length of Lorentz mirror model on the 1D cylinder
• The Boltzmann-Grad Limit of the Lorentz Gas in a Union of Lattices
• Diffusivity of the Lorentz mirror walk in high dimensions
• Probability of hitting a distant point for the voter model started with a single one
• Dimensional crossover via confinement in the lattice Lorentz gas