We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where space possible Dirac operators is assigned a probability distribution. These ensembles are constructed as toy Euclidean quantum gravity on finite spaces and display many interesting properties. The exhibit phase transitions, near these transiti...

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.