10 problems

Let $F_{\beta}(s,m)$ denote the distribution of the $m^{th}$ largest eigenvalue in the appropriate scaling limit for the Gaussian orthogonal ensemble ($\beta=1$) and Gaussian sympl…

The paper considers real eigenpairs of a real antisymmetric tensor of order $p$ and dimension $N$, consisting of a real eigenvalue and $p$ orthonormal $N$-dimensional real eigenvec…

Annular gradient-eigenspectrum conjecture. The particular annular distribution of eigenvalues of the roaRNN gradient helps the learning dynamics to reach a desired eigenspectrum co…

Annular Jacobian distribution conjecture. The characteristic annular distribution of the eigenvalues of the Jacobians may play a key role.

Let $\alpha$ be the parameter of the Chern–Simons matrix model, and consider the limit $\alpha\longrightarrow 0$. Well-behavedness conjecture. The model is perfectly well behaved i…

Gauge-field distribution conjecture. The eigenvalues of the gauge field on the background geometry are also distributed according to this non-polynomial law. The conjecture is moti…

Let $X_1,X_2,\ldots,X_d$ be the $d$ matrices of a reduced Yang–Mills model, and let $R$ be a radius. Uniform-ball conjecture. The joint eigenvalues distribution of…

On the fuzzy-sphere background, the normal scalar field is the normal component of the gauge field, and its eigenvalues follow the non-polynomial law…

Let $X_\mu$, $\mu=1,\ldots,4$, be the four matrices in the matrix phase, and let $R$ be the radius of a solid ball. Four-dimensional uniform-ball conjecture. The joint probability…

Elliptical law. There should be an elliptical law for the eigenvalue distribution, degenerating to the circular law when $\tau=0$.