7 problems

Consider a determinantal point process on the real line with correlation kernel … Label its points by $\cdots<Z_{-1}<Z_0<Z_1<Z_2<\cdots$ so that $Z_{-1}<0\leq Z_0$. The sine-proces…

Let $E$ be the underlying space, let $\mathbb{P}$ be a point process on $E$, and let $\rho^R$ be an $L^1$-specialization. The pair $(\mathbb{P},\rho^R)$ is Giambelli compatible whe…

Optimal-measure claim. For any fixed $n\geq 1$, the optimal measure is $d\sigma=w^\lambda dx$ for some $\lambda\in(-1/2,\infty)$. The value of $\lambda$ may depend on $n$.

Let $A$ be the function defining the Zakharov–Shabat reflection coefficient, let … and let $A_s$ be the associated operator, with kernel $K_s=A_s^2$. Consider the Riemann–Hilbert p…

Let $X$ be the underlying space, let $\mathbb{F}$ be the scalar field, and let $K,Q:X^2\to\mathbb{F}$ be kernels. They are equivalent when, for every $r\geq 1$ and every…

Partial-decoupling conjecture. The kernels of the partial decouplings of $Z$ are the only critical points of $\Phi_{L^*}$.

Uniform Hessian bound. There is a constant $C$, independent of $k$, such that