Multilayer parking with screening on a random tree

TL;DR

This paper introduces a multilayer particle deposition model on random trees, deriving analytical densities, comparing layers and tree types, and revealing higher first-layer densities in random trees.

Contribution

It provides an analytical framework for multilayer deposition on random trees and compares densities across layers and tree structures, highlighting new insights.

Findings

First layer density exceeds second layer density in all trees.

Random trees have higher limiting first layer density than regular trees.

Analytical methods for higher layer densities are proposed.

Abstract

In this paper we present a multilayer particle deposition model on a random tree. We derive the time dependent densities of the first and second layer analytically and show that in all trees the limiting density of the first layer exceeds the density in the second layer. We also provide a procedure to calculate higher layer densities and prove that random trees have a higher limiting density in the first layer than regular trees. Finally, we compare densities between the first and second layer and between regular and random trees.