article
A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
published
yes
Christian
Sadel
author 4760E9F8-F248-11E8-B48F-1D18A9856A870000-0001-8255-3968
Bálint
Virág
author
LaEr
department
International IST Postdoc Fellowship Programme
project
IST Austria Open Access Fund
project
We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix (Formula presented.). Focusing on the eigenvalues of (Formula presented.) of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required (Formula presented.) to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work.
https://research-explorer.app.ist.ac.at/download/1257/5119/IST-2016-703-v1+1_s00220-016-2600-4.pdf
application/pdfno
'https://creativecommons.org/licenses/by/4.0/'
Springer2016
eng
Communications in Mathematical Physics10.1007/s00220-016-2600-4
3433881 - 919
C. Sadel, B. Virág, Communications in Mathematical Physics 343 (2016) 881–919.
Sadel, C., & Virág, B. (2016). A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. <i>Communications in Mathematical Physics</i>, <i>343</i>(3), 881–919. <a href="https://doi.org/10.1007/s00220-016-2600-4">https://doi.org/10.1007/s00220-016-2600-4</a>
Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” <i>Communications in Mathematical Physics</i> 343, no. 3 (2016): 881–919. <a href="https://doi.org/10.1007/s00220-016-2600-4">https://doi.org/10.1007/s00220-016-2600-4</a>.
C. Sadel and B. Virág, “A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes,” <i>Communications in Mathematical Physics</i>, vol. 343, no. 3, pp. 881–919, 2016.
Sadel C, Virág B. 2016. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. 343(3), 881–919.
Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” <i>Communications in Mathematical Physics</i>, vol. 343, no. 3, Springer, 2016, pp. 881–919, doi:<a href="https://doi.org/10.1007/s00220-016-2600-4">10.1007/s00220-016-2600-4</a>.
Sadel C, Virág B. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. <i>Communications in Mathematical Physics</i>. 2016;343(3):881-919. doi:<a href="https://doi.org/10.1007/s00220-016-2600-4">10.1007/s00220-016-2600-4</a>
12572018-12-11T11:50:59Z2020-01-16T12:35:46Z