The 2-torsion of determinantal hypertrees is not Cohen-Lenstra

2024/04/02 by Mészáros, András · 3 citations
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2404.02308

Abstract

Let T_n be a 2-dimensional determinantal hypertree on n vertices. Kahle and Newman conjectured that the p-torsion of H₁(T_n,ℤ) asymptotically follows the Cohen-Lenstra distribution. For p=2, we disprove this conjecture by showing that given a positive integer h, for all large enough n, we have ℙ(dim H₁(T_n,\mathbbF₂)≥ h)≥ \frace^-200h(100h)^5h. We also show that T_n is a bad cosystolic expander with positive probability.

Cited by

• Local limits of determinantal processes
• Using dense graph limit theory to count cocycles of random simplicial complexes
• The fluctuations of the mod p rank of triangular matrices

Related

• The homology torsion growth of determinantal hypertrees
• Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees
• Coboundary expansion for the union of determinantal hypertrees
• Cohen--Lenstra heuristics for torsion in homology of random complexes
• Simplex links in determinantal hypertrees