SEMINAR 2025

Abstract

In this work, we study the dynamics of evolutionary random graphs constructed iteratively from an initial closed structure via probabilistic identification of points on edges for unification, depending on the distance between those edges. The evolution is governed by an infinite-dimensional probability parameter that depends on the geometric and temporal characteristics of the current graph state, such as edge-to-edge distances and restriction for unification per cycle. The focus is on analyzing the asymptotic behavior of such graphs in the limit of many iterations, including degree distributions, connectivity fluctuations, the emergence of critical regimes, and fractal dimensionality.

It is shown that under certain probabilistic control regimes, the model exhibits behavior analogous to that found in discrete approaches to quantum gravity. We discuss the conditions under which the graphs transition into regimes supporting particles and fields on quasi-continuous and cotinious geometries, including possible phase transitions similar to spacetime condensates in Group Field Theory (GFT) and other approaches.

The results can be interpreted as a step toward constructing a probabilistic-geometric model for the emergence of spacetime from discrete dynamical processes and chronostructure. The proposed approach bridges methods from random graph theory, statistical physics, and quantum gravity models within a unified constructive paradigm.