An example of the stochastic dynamics of a causal set

TL;DR

This paper introduces a stochastic model of discrete pregeometry using a directed acyclic graph, demonstrating self-organization through numerical simulations of its growth dynamics.

Contribution

It presents a novel stochastic sequential growth model of a causal set with self-organizing properties, supported by numerical simulation evidence.

Findings

Numerical simulations show signs of self-organization.

The model captures the stochastic dynamics of causal set growth.

It provides insights into microscopic discrete pregeometry structures.

Abstract

An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The particles in this model must be self-organized repetitive structures. The dynamics of this model is a stochastic sequential growth dynamics. New vertexes are added one by one. The probability of this addition depends on the structure of existed graph. The particular case of the dynamics is considered. The numerical simulation provides some symptoms of self-organization.