Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912204442304512 |
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| author | Mészáros, András |
| author_facet | Mészáros, András |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees Mészáros, András Combinatorics Probability 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. |
| title | Bounds on the mod 2 homology of random 2-dimensional determinantal hypertrees |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2401.13646 |