CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution

Details CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution

2010-11-15

arxiv.org/abs/1011.3544v1

Mathematics

Probability

Scientific paper

We show that the global fluctuations of spectra of GOE and GUE matrices and their principal submatrices executing Dyson's Brownian motion are Gaussian in the limit of large matrix dimensions. For nested submatrices one obtains a limiting three-dimensional generalized Gaussian process; its restrictions to two-dimensional sections that are monotone in matrix sizes and time moments coincide with the two-dimensional Gaussian Free Field with zero boundary conditions. The proof is by moment convergence, and it extends to more general Wigner matrices and their stochastic evolution.

Affiliated with

Also associated with

No associations

Rating

CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution 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 CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-463168