# Wegner estimate and Anderson localization for random magnetic fields

Erdös L, Hasler D. 2012. Wegner estimate and Anderson localization for random magnetic fields. Communications in Mathematical Physics. 309(2), 507–542.

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Author

Erdös, László

^{IST Austria}^{}; Hasler, David GAbstract

We consider a two dimensional magnetic Schrödinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i. e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum.

Publishing Year

Date Published

2012-01-01

Journal Title

Communications in Mathematical Physics

Volume

309

Issue

2

Page

507 - 542

IST-REx-ID

### Cite this

Erdös L, Hasler D. Wegner estimate and Anderson localization for random magnetic fields.

*Communications in Mathematical Physics*. 2012;309(2):507-542. doi:10.1007/s00220-011-1373-zErdös, L., & Hasler, D. (2012). Wegner estimate and Anderson localization for random magnetic fields.

*Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-011-1373-zErdös, László, and David Hasler. “Wegner Estimate and Anderson Localization for Random Magnetic Fields.”

*Communications in Mathematical Physics*. Springer, 2012. https://doi.org/10.1007/s00220-011-1373-z.L. Erdös and D. Hasler, “Wegner estimate and Anderson localization for random magnetic fields,”

*Communications in Mathematical Physics*, vol. 309, no. 2. Springer, pp. 507–542, 2012.Erdös, László, and David Hasler. “Wegner Estimate and Anderson Localization for Random Magnetic Fields.”

*Communications in Mathematical Physics*, vol. 309, no. 2, Springer, 2012, pp. 507–42, doi:10.1007/s00220-011-1373-z.