Abstract
We study the level statistics of one-dimensional Schrödinger operator with random potential decaying like x-a at infinity. We consider the point process L consisting of the rescaled eigenvalues and show that: (i) (ac spectrum case) for formula, L converges to a clock process, and the fluctuation of the eigenvalue spacing converges to Gaussian. (ii) (critical case) for formula, L converges to the limit of the circular ß-ensemble.
Original language | English |
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Title of host publication | Festschrift Masatoshi Fukushima |
Subtitle of host publication | In Honor Of Masatoshi Fukushima’s Sanju |
Publisher | World Scientific Publishing Co. |
Pages | 343-373 |
Number of pages | 31 |
ISBN (Electronic) | 9789814596534 |
DOIs | |
Publication status | Published - 2014 Nov 27 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)
- Physics and Astronomy(all)