2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63409In this paper we study the asymptotic behavior for large argument of a family of solutions of the Painlevé equation P$_{\rm VI} arising in the context of Random Matrix Theory [1]. We show this family of solutions are uniquely determined by their asymptotic properties.Classical Analysis and ODEs34M55; 34M30text