# Uniform random colored complexes

## TL;DR

This paper studies random distributions on edge-colored bipartite graphs dual to colored complexes, analyzing their properties and establishing a Central Limit Theorem for the genus of uniform maps as the number of vertices grows large.

## Contribution

It introduces a new probabilistic framework for colored complexes and derives asymptotic properties, including a CLT for genus, expanding understanding of their large-scale behavior.

## Key findings

- Asymptotic behavior of connected components and vertices in random colored complexes
- Establishment of a Central Limit Theorem for the genus of uniform maps
- Insights into the structure of large random colored bipartite graphs

## Abstract

We present here random distributions on $(D+1)$-edge-colored, bipartite graphs with a fixed number of vertices $2p$. These graphs are dual to $D$-dimensional orientable colored complexes. We investigate the behavior of quantities related to those random graphs, such as their number of connected components or the number of vertices of their dual complexes, as $p \to \infty$. The techniques involved in the study of these quantities also yield a Central Limit Theorem for the genus of a uniform map of order $p$, as $p \to \infty$.