Random Sums of Weighted Orthogonal Polynomials in ${\mathbb{C}}^d$

T. Bloom, D. Dauvergne, N. Levenberg

We consider random polynomials of the form $G_n(z):={\sum }_{|\hat{I}\pm |\le n}\hat{I}{¾}_{\hat{I}}^{(n)}\pm p_{n,\hat{I}\pm }(z)$ where $\{\hat{I}{¾}_{\hat{I}}^{(n)}\pm {\}}_{|\hat{I}\pm |\le n}$ are i.i.d. (complex) random variables and $\{p_{…