Geodesic
Gap universality of generalized Wigner and $\beta$-ensembles
Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 1927-2036.

Voir la notice de l'article provenant de la source EMS Press

We consider generalized Wigner ensembles and general β-ensembles with analytic potentials for any β≥1 . The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β-ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact, with an additional step, our result can be extended to any potential C4(R).
DOI : 10.4171/jems/548
Classification : 15-XX, 82-XX
Keywords: β-ensembles, Wigner-Dyson-Gaudin-Mehta universality, gap distribution, log-gas 
@article{JEMS_2015_17_8_a2,
     author = {L\'aszl\'o Erd\H{o}s and Horng-Tzer Yau},
     title = {Gap universality of generalized {Wigner} and $\beta$-ensembles},
     journal = {Journal of the European Mathematical Society},
     pages = {1927--2036},
     publisher = {mathdoc},
     volume = {17},
     number = {8},
     year = {2015},
     doi = {10.4171/jems/548},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/548/}
}
TY  - JOUR
AU  - László Erdős
AU  - Horng-Tzer Yau
TI  - Gap universality of generalized Wigner and $\beta$-ensembles
JO  - Journal of the European Mathematical Society
PY  - 2015
SP  - 1927
EP  - 2036
VL  - 17
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/548/
DO  - 10.4171/jems/548
ID  - JEMS_2015_17_8_a2
ER  - 
%0 Journal Article
%A László Erdős
%A Horng-Tzer Yau
%T Gap universality of generalized Wigner and $\beta$-ensembles
%J Journal of the European Mathematical Society
%D 2015
%P 1927-2036
%V 17
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/548/
%R 10.4171/jems/548
%F JEMS_2015_17_8_a2
László Erdős; Horng-Tzer Yau. Gap universality of generalized Wigner and $\beta$-ensembles. Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 1927-2036. doi : 10.4171/jems/548. http://geodesic.mathdoc.fr/articles/10.4171/jems/548/

Cité par Sources :