Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2401.13646 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- 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.