| Texto completo | |
| Autor(es): |
Alvarado, Jose D.
;
do Couto, Gabriel D.
;
Griffiths, Simon R.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | PROCEEDINGS OF THE 12TH EUROPEAN CONFERENCE ON COMBINATORICS, GRAPH THEORY AND APPLICATIONS, EUROCOMB 2023; v. N/A, p. 8-pg., 2023-01-01. |
| Resumo | |
Two recent papers [11] and [19] study the lower tail of triangle count deviations in random graphs G(n, m) with positive density t := m/((n)(2)) is an element of(0, 1). Let us write D-Delta (G) for the deviation of the triangle count from its mean. Results of [11] and [19] determine the order of magnitude of the log probability log(P (D-Delta(G(n, m)) < -tau ((n)(3)))) for the ranges n(-3/2) << tau << n(-1) and n(-3/4) << tau << 1 respectively. Furthermore, in [19] it is proved that the log probability is at least Omega(tau(2)n(3)) in the "missing" range n(-1) << tau << n(-3/4), and they conjectured that this result gives the correct order of magnitude. Our main contribution is to prove this conjecture. (AU) | |
| Processo FAPESP: | 20/10796-0 - Problemas estruturais em grafos aleatórios |
| Beneficiário: | José Diego Alvarado Morales |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |