Local semicircle law at the spectral edge for Gaussian $β$-ensembles

Details Local semicircle law at the spectral edge for Gaussian $β$-ensembles Local semicircle law at the spectral edge for Gaussian $β$-ensembles

2011-11-05

arxiv.org/abs/1111.1351v1

Mathematics

Probability

16 pages, 2 figures

Scientific paper

We study the local semicircle law for Gaussian $\beta$-ensembles at the edge of the spectrum. We prove that at the almost optimal level of $n^{-2/3+\epsilon}$, the local semicircle law holds for all $\beta \geq 1$ at the edge. The proof of the main theorem relies on the calculation of the moments of the tridiagonal model of Gaussian $\beta$-ensembles up to the $p_n$-moment where $p_n = O(n^{2/3-\epsilon})$. The result is the analogous to the result of Sinai and Soshnikov for Wigner matrices, but the combinatorics involved in the calculations are different.

Affiliated with

Also associated with

No associations

Rating

Local semicircle law at the spectral edge for Gaussian $β$-ensembles 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 Local semicircle law at the spectral edge for Gaussian $β$-ensembles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local semicircle law at the spectral edge for Gaussian $β$-ensembles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-704118