Logarithmic Spectral Distribution of a non-Hermitian $\beta$-Ensemble (opens in new tab)

arXiv:2504.12120v2 Announce Type: replace-cross Abstract: We introduce a non-Hermitian $\beta$-ensemble and determine its spectral density in the limit of large $\beta$ and large matrix size $n$. The ensemble is given by a general tridiagonal complex random matrix of normal and chi-distributed random variables, extending previous work of two of the authors. The joint distribution of eigenvalues contains a Vandermonde determinant to the power $\beta$ and a residual coupling to the eigenvectors...