This is a survey of Harold Widom’s work in random matrices. We start with his pioneering papers on the sine-kernel determinant, continue and Craig Tracy’s groundbreaking results concerning distribution functions matrix theory, touch remarkable universality Tracy–Widom distributions mathematics physics, close Tracy asymmetric simple exclusion process.

Abstract We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of work will appear soon separate publications.) Following an introduction this new type matrices, we focus two specific models matrices are with respect to a given indefinite metric B. Eigenvalues either real, or come complex-conjugat...

We are going to discuss recent progress on many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

We present a systematic construction of probes into the dynamics isospectral ensembles Hamiltonians by notion Isospectral twirling, expanding scopes and methods ref. [1]. The relevant are those defined salient spectral probability distributions. Gaussian Unitary Ensembles (GUE) describes class quantum chaotic Hamiltonians, while spectra corresponding to Poisson Diagonal Ensemble (GDE) describe ...