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.
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.
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