3 problems

Inverse Littlewood–Offord conjecture. If $p_{\mathbf v}$ is large, then most of the elements of $\mathbf v=(v_1,\ldots,v_n)$ belong to a GAP with small rank and small volume. Inver…

Quadratic Littlewood–Offord conjecture. The sharp exponent in the bound for $\mathbb P(F=a)$ should be $-1/2$, meaning that the optimal order is expected to be $O(n^{-1/2})$. The s…

Exponential singularity estimate conjecture. An exponential-type estimate on the singularity probability of $A_n$ can be proven whenever