3 problems

Let $\mu$ be either the sine$_2$ point process or the Airy$_2$ point process, and let $\nu$ be a probability measure on the configuration space $\boldsymbol\Upsilon$. Suppose that…

Number-rigidity conjecture. Number-rigidity should occur for $s\leq d-1$ at any dimension $d$.

Let $X$ be a point process, and let $N_\Lambda$ denote the number of points of $X$ in a bounded region $\Lambda$. The process is number rigid if $N_\Lambda$ is determined by the co…