7 problems

Basor–Tracy conjecture. As $n\to\infty$,

Generalized Fisher–Hartwig conjecture. The determinant ratio satisfies

Let $\chi(\kappa,x)$ have the asymptotic expansion … where $L_j(\kappa,x)$ are Laurent series in $x$. All-orders periodicity conjecture. For every order in the $1/x$ expansion, the…

Let $\chi(\kappa,x)$ have the Fisher–Hartwig asymptotic expansion given by Eqs. (GFH-1)–(GFH-2), and let the coefficients be defined for values of $\kappa$ away from the lines…

Let $\chi(\kappa,x)$ be the double-scaling limit of the Toeplitz determinant, with asymptotic expansion … where $L_j(\kappa,x)$ are Laurent series in $x$ whose coefficients depend…

Let $D_N$ be a Toeplitz determinant with Fisher–Hartwig branches, and let $N$ tend to infinity. For each branch, consider its asymptotic expansion in powers of $1/N$. Full-branch c…

Let $D_N$ be a Toeplitz determinant whose asymptotics are described by multiple Fisher–Hartwig branches, and let $N$ tend to infinity. Subleading-branch conjecture. Subleading Fish…