Decoupling inequalities with exponential constants

Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means standard tools from the theory independent variables. We study decoupling for vector-valued homogeneous polynomials evaluated at focus on providing geometric conditions ensuring with good constants depending only exponentially degree polynomial. Assuming Banach space has finite cotype we achieve this classical compare their associated multilinear operators. Under stronger assumptions involved spaces, also obtain between and fully sums coefficients. Finally, present where in operator just two copies vector are involved.