arXiv subjects

Seungjoon Oh

Publications and source records attributed to Seungjoon Oh.

3 recordsLinked to original sources

arXiv2026

Dissipative Spectral Form Factor of the Complex Elliptic Ginibre Ensemble across Various Non-Hermiticity Regimes

We study the dissipative spectral form factor (DSFF) at complex time $T e^{i\theta}$ for the complex elliptic Ginibre ensemble with non-Hermiticity parameter $\tau \in [0,1)$. As the matrix dimension $N \to \infty$, we consider the natural scalings in both the time variable and the non-Hermiticity parameter, namely $T = O(N^\gamma)$ and $1 - \tau = O(N^{-\alpha})$. For all regimes $\gamma \ge 0$ and $\alpha \ge 0$, we derive the precise asymptotic behaviour of both the disconnected and connected components of the DSFF. In particular, we explicitly characterise the dip--ramp--plateau structure, including the dip time and the Heisenberg time. In addition, we identify the mesoscopic regime $\alpha \in (0,1)$, which interpolates between the behaviour of the DSFF of non-Hermitian random matrices and the spectral form factor (SFF) of Hermitian ensembles. We further provide an explicit description of the phase diagram, in which the ramp exhibits quadratic, linear, or intermediate behaviour depending on the scaling parameters.

math-ph↗

arXiv2026

Spectral moments of complex and symplectic non-Hermitian random matrices

We study non-Hermitian random matrices belonging to the symmetry classes of the complex and symplectic Ginibre ensemble, and present a unifying and systematic framework for analysing mixed spectral moments involving both holomorphic and anti-holomorphic parts. For weight functions that induce a recurrence relation of the associated planar orthogonal polynomials, we derive explicit formulas for the spectral moments in terms of their orthogonal norms. This includes exactly solvable models such as the elliptic Ginibre ensemble and non-Hermitian Wishart matrices. In particular, we show that the holomorphic spectral moments of complex non-Hermitian random matrices coincide with those of their Hermitian limit up to a multiplicative constant, determined by the non-Hermiticity parameter. Moreover, we show that the spectral moments of the symplectic non-Hermitian ensemble admit a decomposition into two parts: one corresponding to the complex ensemble and the other constituting an explicit correction term. This structure closely parallels that found in the Hermitian setting, which naturally arises as the Hermitian limit of our results. Within this general framework, we perform a large-$N$ asymptotic analysis of the spectral moments for the elliptic Ginibre and non-Hermitian Wishart ensemble, revealing the mixed moments of the elliptic and non-Hermitian Marchenko--Pastur laws. Furthermore, for the elliptic Ginibre ensemble, we employ a recently developed differential operator method for the associated correlation kernel, to derive an alternative explicit formula for the spectral moments and obtain their genus-type large-$N$ expansion.

math-ph↗

arXiv2026

Upper tail large deviations for extremal eigenvalues of the real, complex and symplectic elliptic Ginibre matrices

We consider the elliptic Ginibre ensembles in the real, complex and symplectic symmetry classes. As the matrix size tends to infinity, we derive the asymptotic behaviour of the upper tail large deviation probabilities for both the spectral radius and the rightmost eigenvalue. More generally, we obtain asymptotic formulas for the probability that an eigenvalue is found in a prescribed region outside the support of the elliptic law, thereby providing a unified framework in which the results for the spectral radius and the rightmost eigenvalue appear as special cases. The key ingredient of our analysis is the precise asymptotic behaviour of the associated one-point functions, which is of independent interest.

math.PR↗