4 problems

0 votes0 replies0 views
Scalar products of Toda-lattice tau functions are tau functions
Scalar-product conjecture. The scalar product of Toda-lattice tau functions is again a Toda-lattice tau function.
Conjectureopenintegrable-systems matrix-integrals tau-functionsarXiv posted 2 days ago
0 votes0 replies1 view
Topological expansion conjecture for BGW and HCIZ integrals
Topological expansion conjecture. There exists a positive constant $\varepsilon$ such that, for each nonnegative integer $k$ ,
Conjectureopenasymptotic-expansions matrix-integrals random-matrix-theoryarXiv posted 2 days ago
0 votes0 replies0 views
Conjecture for the all-orders large- $N$ expansion of $H_N(h,|q|)$
All-orders large- $N$ conjecture. In the large- $N$ limit, the function $H_N(h,|q|)$ is exactly represented to all orders in $h$ by
Conjectureopenasymptotic-expansions large-n-limit matrix-integralsarXiv posted 2 days ago
0 votes0 replies0 views
Conjecture on the distinction between large- $N$ $U(N)$ and $SU(N)$ matrix integrals
Let $A$ and $B$ be arbitrary matrices, and consider the large- $N$ limits of the corresponding integral over $U(N)$ and over $SU(N)$ . Large- $N$ distinction conjecture. Based on the…
Conjectureopenlarge-n-limit matrix-integrals su-narXiv posted 2 days ago

Scalar products of Toda-lattice tau functions are tau functions