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We consider the Cauchy problem for the fourth order nonlinear Schr\"{o}dingerequation with derivative nonlinearity $(i\partial _t + \Delta ^2) u= \pm\partial (|u|^2u)$ on $\mathbb{R} ^d$, $d \ge 3$, with random initial data,where $\partial$ is a first order derivative with respect to the spatialvariable, for example a linear combination of $\frac{\partial}{\partial x_1} ,\, \dots , \, \frac{\partial}{\partial x_d}$ or $|\nabla |=\mathcal{F}^{-1}[|\xi | \mathcal{F}]$. We prove that almost sure local in timewell-posedness, small data global in time well-posedness and scattering hold in$H^s(\mathbb{R} ^d)$ with $\max ( \frac{d-5}{2}, \frac{d-5}{6}) < s$, whoselower bound is below the scale critical regularity $s_c= \frac{d-3}{2}$.

Random data Cauchy theory for the fourth order nonlinear Schr\"{o}dinger equation with cubic nonlinearity