An aspect of particles' spatial competition
Achillefs Tzioufas
TL;DR
This paper explores the spatial competition among particles in branching random walks, revealing monotonicity properties and percolation path behaviors on lattices, contributing to understanding particle lineage and lattice percolation.
Contribution
It introduces new monotonicity results for branching random walks and percolation paths based on antisymmetric initial states.
Findings
Branching random walk is monotone decreasing in the lattice's ascending direction.
Lineage of particles from antisymmetric initial states exhibits specific properties.
Percolation paths on oriented lattices have related monotonicity properties.
Abstract
The branching random walk is shown to be monotone decreasing in ascending direction of integer lattices as a corollary of an observation in regard to the lineage of particles from antisymmetric initial states, and a related property of percolation paths on the usual oriented lattices is also given.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Random Matrices and Applications