Let $\mathcal{G}$ be a $k$-player game with value $<1$, whose query distribution is such that no marginal on $k-1$ players admits a non-trivial Abelian embedding. We show that for every $n\geq N$, the value of the $n$-fold parallel repetition of $\mathcal{G}$ is $$ \text{val}(\mathcal{G}^{\otimes n}) \leq \frac{1}{\underbrace{\log\log\cdots\log}_{C\text{ times}} n}, $$ ... more >>>

In this work, we give an optimal analysis of the plane versus plane test of Raz and Safra (STOC'97). More specifically, consider a table $T$ that assigns every plane $P$ from $\mathbb{F}_q^m$ a bivariate degree $d$ polynomial. The goal is to check if these polynomials are restrictions of a global ... more >>>