Feynman checkers: the probability to find an electron vanishes nowhere inside the light cone

TL;DR

This paper analyzes Feynman checkers, demonstrating that the probability of finding an electron is non-zero everywhere inside the light cone, and explores related properties like average velocity and mathematical identities.

Contribution

It provides rigorous proofs that the electron probability density never vanishes inside the light cone in the Feynman checker model, along with new identities and velocity results.

Findings

Probability to find an electron is non-zero inside the light cone

Several identities related to the Feynman checker model are established

Results on the average electron velocity are presented

Abstract

We study Feynman checkers, the most elementary model of electron motion introduced by R. Feynman. For the model, we prove that the probability to find an electron vanishes nowhere inside the light cone. We also prove several results on the average electron velocity. In addition, we present a lot of identities related to the model.