Connes' Bicentralizer Problem for Mixed $q$-deformed Araki-Woods Algebras

In this article, we show that the mixed $q$-deformed Araki-Woods von Neumann algebra ${\mathrm{\Gamma }}_T(H_{\mathbb{R}},U_t{)}^{\mathrm{\prime }\mathrm{\prime }}$ has trivial bicentralizer, whenever it is of type ${\mathrm{I}\mathrm{I}\mathrm{I}}_1$.