3 problems

Convergent matrix-integral decomposition conjecture. The convergent matrix integral $Z_{\rm conv}$ is a finite linear combination of convergent formal solutions of the loop equatio…

Let $\beta>0$, and let $s$ be a random particle-generated Nevanlinna function satisfying the bulk condition in or the edge condition in. Under either condition, the poles of $s$ de…

Let $F_{g,n}$ be the free-energy generating functions associated with the double Hurwitz numbers, let $a_1,\ldots,a_d$ be the branch points of the spectral curve, and let…