TY - JOUR
T1 - Gaussian Beta Ensembles at High Temperature
T2 - Eigenvalue Fluctuations and Bulk Statistics
AU - Nakano, Fumihiko
AU - Trinh, Khanh Duy
N1 - Funding Information:
This work is partially supported by JSPS KAKENHI Grant Numbers JP26400145 (F.N.) and JP16K17616 (K.D.T).
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - We study the limiting behavior of Gaussian beta ensembles in the regime where βn= const as n→ ∞. The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by Benaych-Georges and Péché (J Stat Phys 161(3):633–656, 2015) with the explicit form of the intensity measure.
AB - We study the limiting behavior of Gaussian beta ensembles in the regime where βn= const as n→ ∞. The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by Benaych-Georges and Péché (J Stat Phys 161(3):633–656, 2015) with the explicit form of the intensity measure.
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U2 - 10.1007/s10955-018-2131-9
DO - 10.1007/s10955-018-2131-9
M3 - Article
AN - SCOPUS:85051680090
SN - 0022-4715
VL - 173
SP - 295
EP - 321
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
ER -