Topology and geometry of random 2-dimensional hypertrees

2020/04/28 by Kahle, Matthew, Newman, Andrew · 4 citations
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.13572

Abstract

A hypertree, or ℚ-acyclic complex, is a higher-dimensional analogue of a tree. We study random 2-dimensional hypertrees according to the determinantal measure suggested by Lyons. We are especially interested in their topological and geometric properties. We show that with high probability, a random 2-dimensional hypertree T is apsherical, i.e. that it has a contractible universal cover. We also show that with high probability the fundamental group π₁(T) is hyperbolic and has cohomological dimension 2.

Cited by

• Using dense graph limit theory to count cocycles of random simplicial complexes
• Cohen-Lenstra flag universality for random matrix products
• The fluctuations of the mod p rank of triangular matrices
• The homology torsion growth of determinantal hypertrees

Related

• Simplex links in determinantal hypertrees
• Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees
• Enumeration and randomized constructions of hypertrees
• Random Trees in Hyperbolic FPP
• Using dense graph limit theory to count cocycles of random simplicial complexes