2013 Fiscal Year Final Research Report
Level Statistics for Random Schroedinger Operators
| Project/Area Number |
22540140
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Gakushuin University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MINAMI Nariyuki 慶応大学, 医学部, 教授 (10183964)
UEKI Naomasa 京都大学, 人間環境学研究科, 教授 (80211069)
SADAHIRO Taizo 津田塾大学, 学芸学部, 准教授 (00280454)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | ランダムシュレーディンガー作用素 / 準位統計 / ランダム行列 |
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| Research Abstract |
We study the level statistics problem for 1-dimensional Schroedinger operators with random decaying potential. That is, we restrict our Hamiltonian on a bounded interval, consider a point process composed of the rescaled eigenvalues of this truncated Hamiltonian, and then study its infinite volume limit. The result is : (i) rapid decay case : the point process converges to the clock process, and second order asymptotics converges to Gaussian, (ii) critical decay case : the point process converges to that of the circular beta ensemble, as well as that of the Gaussian beta ensemble, thus yielding the coincidence of these two processes as a corollary.
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