Stretch IDLA
Noam Berger, Jacob J. Kagan, Eviatar B. Procaccia
TL;DR
This paper introduces a new IDLA particle system model on the upper half planar lattice, forming an infinite forest, and proves that all trees in this forest are finite with probability one.
Contribution
The paper presents a novel IDLA model on the half-plane and establishes the finiteness of all trees in the resulting infinite forest.
Findings
All trees in the infinite forest are finite almost surely.
The model extends IDLA theory to the half-plane setting.
The structure of the forest is rigorously characterized.
Abstract
We consider a new IDLA - particle system model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. We prove that almost surely all trees are finite.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Quantum Chromodynamics and Particle Interactions