2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216873We clarify the asymptotic of the limsup of the size of the neighborhood of concentration of Sinai's walk improving the result in \cite{Pierre3}. Also we get the almost sure limit of the number of points visited more than a small but fixed proportion of a given amount of time.Probability60G50, 60J55Constants of concentration for a simple recurrent random walk on random environmenttext