Random matrix

[edit] Random matrix theory topics

Spectral theory of random matrices
Free probability
Determinantal ensembles
Integral operators in random matrix theory
Dyson processes. Airy, Bessel, sine and Laguerre processes
Matrix Riemann-Hilbert methods, applications to large N asymptotics
Differential equations for gap distributions and transition probabilities
Relations to integrable systems and isomonodromic deformations
Growth processes; applications to fluid dynamics and crystal growth
Applications to random tilings, random words, random partitions
Applications to L-functions, including support for the Hilbert-Pólya conjecture.
Applications to multivariate statistics
Applications to nuclear physics, including the Gaussian unitary ensemble, the Gaussian symplectic ensemble, and the Gaussian orthogonal ensemble. The spectra and cross sections nuclei measured in laboratories show that the dynamics of the nucleus is exceedingly complex. Evidence points at a chaotic behaviour similar to that seen on hyperbolic manifolds; random matrix theory attempts to model the gross properties of the nuclear spectra (distribution of resonances, spectral line widths) through ensembles of random matrices.
Applications to signal processing and wireless communications
Applications to quantum chaos and mesoscopic physics