Particle Systems with Stochastic Passing
Abstract
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P0(v), while the slow particle remains unaffected. We show that the system reaches a steady state if P0(v) vanishes at its lower cutoff; otherwise, the system evolves indefinitely.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.