Universality of the distribution functions of random matrix theory. (English) Zbl 0973.60057
Harnad, J. (ed.) et al., Integrable systems: from classical to quantum. Proceedings of the 38th session of the Séminaire de mathématiques supérieures, Montréal, Canada, July 26-August 6, 1999. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 26, 251-264 (2000).
Summary: We give a brief overview of some recent developments in random matrix theory. The focus is on various scaling limits and the associated limiting distribution functions. These limiting distributions are expressible in terms of solutions to integrable differential equations of the Painlevé type. The universality of these limiting laws is discussed.
For the entire collection see [Zbl 0952.00031].
For the entire collection see [Zbl 0952.00031].
MSC:
| 60G70 | Extreme value theory; extremal stochastic processes |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 47B99 | Special classes of linear operators |
| 34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
