Random Matrix - Applications

Applications

• 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 magnetic systems, such as magnetic multilayers, the quantum Hall effect, quantum dots, and superconductors.
• 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
• Applications to number theory
• Applications to operator algebras, and free probability .
• Applications to models of quantum gravity in two dimensions
• Current research suggests it could have applications in improving web search engines