3 problems

Let $P(s)$ be the probability that there are no bulk GUE eigenvalues in the interval $\left(-\frac{s}{\pi},\frac{s}{\pi}\right)$, and let $c_0$ be a constant. Dyson's conjecture. A…

Let $t$ denote the endpoint of a hard- or soft-edge gap in a general $\beta$-ensemble, and condition on there being $n$ eigenvalues in the gap, with $n\ll |t|$. Consider the derive…

Let $\mu(\tau)$ denote the parameter-dependent quantity in the interpolating random-matrix ensemble, and let the even and odd terms refer to products formed from the even- and odd-…