Continuum limits of random matrices and the Brownian carousel

Details Continuum limits of random matrices and the Brownian carousel Continuum limits of random matrices and the Brownian carousel

2007-12-12

arxiv.org/abs/0712.2000v4

Invent. Math. 177 (2009), no. 3, 463-508

Mathematics

Probability

53 pages, 3 figures, We corrected some typos and minor mistakes. Some parts have been revised/extended to make them clearer, e

Scientific paper

10.1007/s00222-009-0180-z

We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general beta siblings converge to Sine_beta, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We show that the gap probability of Sine_beta is continuous in the gap size and $\beta$, and compute its asymptotics for large gaps. Moreover, the stochastic differential equation version of the Brownian carousel exhibits a phase transition at beta=2.

Affiliated with

Also associated with

No associations

Rating

Continuum limits of random matrices and the Brownian carousel does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Continuum limits of random matrices and the Brownian carousel, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuum limits of random matrices and the Brownian carousel will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-662080