Improved Depth-2 Linear Circuits for Disjointness via Quenched Lyapunov Exponents

Let $R_1 := \begin{pmatrix}1&1\\1&0\end{pmatrix}$, and write $R_n := R_1^{\otimes n}$ for the $N \times N$ disjointness matrix, where $N = 2^n$. We construct new depth-2 linear circuits for $R_n$: one of size $O(N^{1.2449})$ and one of maximum input-output degree $O(N^{0.3199})$, improving upon the