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arXiv · 2401.13646

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

András Mészáros
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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 \[\frac{\dim H_1(T_n,\mathbb{F}_2)}{n^2}\] 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.

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András Mészáros. 2025-01-27. Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees. https://arxiv.org/abs/2401.13646

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