dc.creator | Swan, Andrew | |
dc.creator | Olver, Sheehan | |
dc.date.accessioned | 2017-11-05 | |
dc.date.accessioned | 2018-11-24T23:20:52Z | |
dc.date.available | 2018-03-02T16:15:47Z | |
dc.date.available | 2018-11-24T23:20:52Z | |
dc.identifier | https://www.repository.cam.ac.uk/handle/1810/273716 | |
dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3660 | |
dc.description.abstract | We prove that the Poisson/Gaudin--Mehta phase transition conjectured to occur when the bandwidth of an N ⨯ N symmetric band matrix grows like b = √N is naturally observable in the rate of convergence of the level density to the Wigner semi-circle law. Specifically, we show for periodic and non-periodic band matrices the rate of convergence of the fourth moment of the level density is independent of the boundary conditions in the localised regime b << √N with a rate of O(1/b) for both cases, whereas in the delocalised regime b >> √N where boundary effects become important, the rate of convergence for the two ensembles differ significantly, slowing to O(b/N) for non-periodic band matrices. Additionally, we examine the case of thick non-periodic band matrices b = cN, showing that the fourth moment is maximally deviated from the Wigner semi-circle law when b = 2N/5, and provide numerical evidence that the eigenvector statistics also exhibit critical behaviour at this point. | |
dc.publisher | Random Matrices: Theory and Applications | |
dc.rights | http://creativecommons.org/licenses/by/4.0/ | |
dc.rights | Attribution 4.0 International | |
dc.title | Evidence for the Poisson/Gaudin--Mehta phase transition for band matrices on global scales | |
dc.type | Article | |