Random simplicial complexes - around the phase transition

TL;DR

This paper surveys recent research on random simplicial complexes, focusing on phase transitions in higher-dimensional analogs of Erdős–Rényi graphs, aiming to unify and clarify the current understanding of these phenomena.

Contribution

It offers a streamlined, unified overview of recent developments in the study of phase transitions in random simplicial complexes.

Findings

Identification of phase transition thresholds in higher dimensions

Unified perspective on various models and results

Clarification of the behavior of topological properties near critical points

Abstract

This article surveys some of the work done in recent years on random simplicial complexes. We mostly consider higher-dimensional analogs of the well known phase transition in $G(n, p)$ theory that occurs at $p = \frac 1n$ . Our main objective is to provide a more streamlined and unified perspective of some of the papers in this area.