4 problems

The paper considers dependent stochastic processes with clustering effects and an extremal index controlling extreme-value statistics. Applicability conjecture. The conditions deve…

Uniqueness conjecture. The $1$-dependent $4$-coloring is unique.

Schramm's operator conjecture. Such $U$ and $R$ cannot exist for any $k$ and $q$, even if the $U_j$ are merely linearly independent and the separability restriction is removed.

Schramm's conjecture. No stationary $k$-dependent $q$-coloring of $\mathbb Z$ exists for any positive integers $k$ and $q$.