Semantic Scholar Open Access 2011 13 sitasi

Local Semicircle Law in the Bulk for Gaussian β-Ensemble

Philippe Sosoe Percy Wong

Abstrak

We use the tridiagonal matrix representation to derive a local semicircle law for Gaussian beta ensembles at the optimal level of n−1+δ for any δ>0. Using a resolvent expansion, we first derive a semicircle law at the intermediate level of n−1/2+δ; then an induction argument allows us to reach the optimal level. This result was obtained in a different setting, using different methods, by Bourgade, Erdös, and Yau in arXiv:1104.2272 [math.PR] and Bao and Su in arXiv:1104.3431 [math.PR]. Our approach is new and could be extended to other tridiagonal models.

Topik & Kata Kunci

Mathematics

Penulis (2)

Philippe Sosoe

Percy Wong

Format Sitasi

APA MLA BibTeX

Sosoe, P., Wong, P. (2011). Local Semicircle Law in the Bulk for Gaussian β-Ensemble. https://doi.org/10.1007/s10955-012-0536-4

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Informasi Jurnal

Tahun Terbit: 2011
Bahasa: en
Total Sitasi: 13×
Sumber Database: Semantic Scholar
DOI: 10.1007/s10955-012-0536-4
Akses: Open Access ✓