This paper studies the quintic nonlinear Schrödinger equation on
${\mathbb{R}}^{d}$
with randomized initial data below the critical regularity
${H}^{\left(d1\right)\u22152}$ for
$d\ge 3$. The main
result is a proof of almost sure local wellposedness given a Wiener randomization of the
data in
${H}^{s}$
for
$s\in \left(\frac{1}{2}\left(d2\right),\frac{1}{2}\left(d1\right)\right)$.
The argument further develops the techniques introduced in the work of Á. Bényi,
T. Oh and O. Pocovnicu on the cubic problem. The paper concludes with a
condition for almost sure global wellposedness.
