Maps on random hypergraphs and random simplicial complexes

TL;DR

This paper investigates the properties of random sub-hypergraphs and sub-complexes of a given simplicial complex, focusing on maps defined by embedding minimal and maximal complexes, and analyzes their compositions and effects on probability functions.

Contribution

It introduces new maps on the space of probability functions related to embeddings of sub-hypergraphs and sub-complexes, exploring their compositions and actions.

Findings

Defined maps based on minimal and maximal embeddings

Analyzed compositions of these maps

Studied their effects on probability functions

Abstract

Let $L$ be a simplicial complex. In this paper, we study random sub-hypergraphs and random sub-complexes of $L$. By considering the minimal complex that a sub-hypergraph can be embedded in and the maximal complex that can be embedded in a sub-hypergraph, we define some maps on the space of probability functions on sub-hypergraphs of $L$. We study the compositions of these maps as well as their actions on the space of probability functions.