Random matrix theory

History

Random matrix theory first gained attention beyond mathematics literature in the context of nuclear physics. Experiments by Enrico Fermi and others demonstrated evidence that individual nucleons cannot be approximated to move independently, leading Niels Bohr to formulate the idea of a compound nucleus. Because there was no knowledge of direct nucleon-nucleon interactions, Eugene Wigner and Leonard Eisenbud approximated that the nuclear Hamiltonian could be modeled as a random matrix. For larger atoms, the distribution of the energy eigenvalues of the Hamiltonian could be computed in order to approximate scattering cross sections by invoking the Wishart distribution.