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

Mészáros, András (2025) Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees. COMBINATORICA, 45 (2). ISSN 0209-9683

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Abstract

As a first step towards a conjecture of Kahle and Newman, we prove that if Tn is a random 2-dimensional determinantal hypertree on n vertices, then dimH1(Tn,F2)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.

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