3 problems

Let $f$ be a Gaussian field with covariance kernel $r\in L^1(\mathbb{R}^d)$. Suppose the upper bound in Theorem number-count is considered for the corresponding number of high loca…

KKLS conjecture. For $1<r<r_{\max}(12)$, there are other sharp locally maximal clusters of $12$ balls of radius $r$, besides the known examples.

Let $f$ be an isotropic Gaussian field on the sphere satisfying conditions $({\bf C}1')$, $({\bf C}2')$ and $({\bf C}3')$ in Cheng and Schwartzman (2015), and let $\kappa_1$ and…