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In 1962, Dyson introduced dynamics in random matrix models, in particular into GUE (also for beta=1 and 4), by letting the entries evolve according to independent Ornstein-Uhlenbeck processes.
On the theory of the brownian motion
G. E. Uhlenbeck and L. S. Ornstein · 1930
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A Brownian-motion model for the eigenvalues of a random matrix
Freeman J. Dyson · 1962
Earlier work this paper cites.
Stochastic integrals
Henry P. McKean · 1969
Earlier work this paper cites.
An introduction to probability theory and its applications. Vol. II
William Feller · 1971
Earlier work this paper cites.
Matrix Theory
Madan Lal Mehta · 1988
Earlier work this paper cites.
Multilevel dynamical correlation functions for Dyson’s Brownian motion model of random matrices
Taro Nagao and Peter J. Forrester · 1998
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Non-intersecting paths, random tilings and random matrices
Kurt Johansson · 2002
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A path-transformation for random walks and the Robinson-Schensted correspondence
Neil O’Connell · 2003
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Stochastic differential equations
Bernt Øksendal · 2003
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Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
Makoto Katori and Hideki Tanemura · 2004
Cited alongside, same era.
Random matrices
Madan Lal Mehta · 2004
Cited alongside, same era.
Differential equations for Dyson processes
Craig A. Tracy and Harold Widom · 2004
Cited alongside, same era.
PDEs for the joint distributions of the Dyson, Airy and sine processes
Mark Adler and Pierre van Moerbeke · 2005
Cited alongside, same era.
The arctic circle boundary and the Airy process
Kurt Johansson · 2005
Cited alongside, same era.
Dyson’s Brownian motions, intertwining and interlacing
Jon Warren · 2007
Later among the works it cites.
Orbit measures and interlaced determinantal point processes
Manon Defosseux · 2008
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Orbit measures, random matrix theory and interlaced determinantal processes
Manon Defosseux · 2008
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Maximum of Dyson Brownian motion and non-colliding systems with a boundary
Alexei Borodin, Patrik L. Ferrari, Michael Prähofer, Tomohiro Sasamoto, and Jon Warren · 2009
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Random walks conditioned to stay in Weyl chambers of type C and D
Wolfgang König and Patrik Schmid · 2009
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Kurt Johansson · 2005
Cited alongside, same era.
Eigenvalues of GUE minors
Kurt Johansson and Eric Nordenstam · 2006
Cited alongside, same era.
Interlaced processes on the circle
Anthony P. Metcalfe, Neil O’Connell, and Jon Warren · 2009
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The Dyson Brownian minor process
Mark Adler, Eric Nordenstam, and Pierre van Moerbeke · 2010
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On the shuffling algorithm for domino tilings
Eric Nordenstam · 2010
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