Renormalized energy concentration in random matrices

Details Renormalized energy concentration in random matrices Renormalized energy concentration in random matrices

2012-01-13

arxiv.org/abs/1201.2853v2

Mathematics

Probability

44 pages, 2 figures

Scientific paper

We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of [SS1,SS3]. Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix $\beta$-sine processes on the real line (beta=1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the beta=2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.

Affiliated with

Also associated with

No associations

Rating

Renormalized energy concentration in random matrices 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 Renormalized energy concentration in random matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Renormalized energy concentration in random matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-471761