# Volumes of random 3-manifolds

## TL;DR

This paper establishes a law of large numbers for the volumes of random hyperbolic 3-manifolds, confirming a conjecture and providing precise asymptotic behavior for these geometric structures.

## Contribution

It proves a law of large numbers for volumes of random hyperbolic 3-manifolds, resolving a conjecture by Dunfield and Thurston.

## Key findings

- Volumes of random hyperbolic mapping tori follow a predictable asymptotic distribution.
- The results provide a sharp quantitative understanding of volume growth in random 3-manifolds.
- Confirmation of the conjecture by Dunfield and Thurston regarding volume behavior.

## Abstract

We prove a law of large numbers for the volumes of families of random hyperbolic mapping tori and Heegaard splittings providing a sharp answer to a conjecture of Dunfield and Thurston.