A sequential growth dynamics for a directed acyclic dyadic graph

Abstract

A model of discrete spacetime on a microscopic level is considered. It is a directed acyclic dyadic graph. This is the particular case of a causal set. The goal of this model is to describe particles as some repetitive symmetrical self-organized structures of the graph without any reference to continuous spacetime. The dynamics of the model is considered. This dynamics is stochastic sequential additions of new vertexes. Growth of the graph is a Markovian process. This dynamics is a consequence of a causality principle.