Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees

2024/01/24 by Mészáros, András · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.13646

Abstract

As a first step towards a conjecture of Kahle and Newman, we prove that if T_n is a random 2-dimensional determinantal hypertree on n vertices, then \fracdim H₁(T_n,\mathbbF₂)n² converges to zero in probability. Confirming a conjecture of Linial and Peled, we also prove the analogous statement for the 1-out 2-complex. Our proof relies on the large deviation principle for the Erdős-Rényi random graph by Chatterjee and Varadhan.

Cited by

• Local limits of determinantal processes
• Using dense graph limit theory to count cocycles of random simplicial complexes

Related

• The homology torsion growth of determinantal hypertrees
• Using dense graph limit theory to count cocycles of random simplicial complexes
• Topology and geometry of random 2-dimensional hypertrees
• Enumeration and randomized constructions of hypertrees
• The 2-torsion of determinantal hypertrees is not Cohen-Lenstra