• journal/journal.article
• aip/jmp
• /content/aip/journal/jmp/54/3/10.1063/1.4794082
1887
No data available.
No metrics data to plot.
The attempt to plot a graph for these metrics has failed.
f

### Optimal volume Wegner estimate for random magnetic Laplacians on <mml:math> <mml:msup> <mml:mrow> <mml:mi>Z</:mi> </:mrow> <mml:mn>2</:mn> </:msup> </:math> \$(document).ready(function() { // The supplied crossmark code loads this inline before jqplot has finished unitialising, they then unregister the // jQuery causing much hilarity - doing it after page load is safer, we chain all of our requests to hopefully avoid // any kind of race condition var cachedScript = jQuery.cachedScript; cachedScript("https://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js", { success: function () { cachedScript("https://ajax.googleapis.com/ajax/libs/jqueryui/1.8.7/jquery-ui.min.js", { success: function () { var s = document.createElement('script'); s.type = 'text/javascript'; s.src = 'http://crossmark.crossref.org/javascripts/v1.3/crossmark.min.js'; document.body.appendChild(s); } }); } }); });

Access full text Article
View Affiliations Hide Affiliations
Affiliations:
1 Department of Mathematics, Friedrich-Schiller-University Jena, Jena, Germany
2 Department of Mathematics, College of William & Mary, Williamsburg, Virginia, USA
J. Math. Phys. 54, 032105 (2013)
/content/aip/journal/jmp/54/3/10.1063/1.4794082

### References

• David Hasler and Daniel Luckett
• Source: J. Math. Phys. 54, 032105 ( 2013 );
1.
1. Bourgain, J. and Klein, A. , “Bounds on the density of states for Schrödinger operators,” e-print arXiv:1112.1716.
2.
2. Carmona, R. and Lacroix, J. , Spectral Theory of Random Schrödinger Operators, Probability and its Applications (Birkhäuser, Boston, MA, 1990).
3.
3. Combes, J.-M. and Hislop, P. , “Landau Hamiltonians with random potentials: Localization and the density of states,” Commun. Math. Phys. 177, 603629 (1996).
http://dx.doi.org/10.1007/BF02099540
4.
4. Combes, J.-M. , Hislop, P. , and Klopp, F. , “An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators,” Duke Math. J. 140(3), 469498 (2007).
http://dx.doi.org/10.1215/S0012-7094-07-14032-8
5.
5. Combes, J.-M. , Hislop, P. , and Klopp, F. , “Hölder continuity of the integrated density of states for some random operators at all energies,” Int. Math. Res. Notices 2003(4), 179209.
http://dx.doi.org/10.1155/S1073792803202099
6.
6. Combes, J.-M. , Hislop, P. , Klopp, F. , and Raikov, G. , “Global continuity of the integrated density of states for random Landau Hamiltonians,” Commun. Partial Differ. Equ. 29(7–8), 11871213 (2004).
http://dx.doi.org/10.1081/PDE-200033731
7.
7. Craig, W. and Simon, B. , “Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices,” Commun. Math. Phys. 90(2), 207218 (1983).
http://dx.doi.org/10.1007/BF01205503
8.
8. Delyon, F. , Francois, G. , and Souillard, B. , “Remark on the continuity of the density of states of ergodic finite difference operators,” Commun. Math. Phys. 94(2), 289291 (1984).
http://dx.doi.org/10.1007/BF01209306
9.
9. Erdős, L. and Hasler, D. , “Wegner estimate and Anderson localization for random magnetic fields,” Comm. Math. Phys. 309(2), 507542 (2012);
http://dx.doi.org/10.1007/s00220-011-1373-z
9.e-print arXiv:1012.5185.
10.
10. Erdős, L. and Hasler, D. , “Wegner estimate for random magnetic Laplacians on ,” Ann. Henri Poincare 12, 17191731 (2012).
http://dx.doi.org/10.1007/s00023-012-0177-9
11.
11. Ghribi, F. , Hislop, P. D. , and Klopp, F. , “Localization for Schrödinger operators with random vector potentials,” in Adventures in Mathematical Physics (Contemp. Math.) (Amer. Math. Soc., Providence, RI, 2007), Vol. 447, pp. 123138.
12.
12. Hislop, P. D. and Klopp, F. , “The integrated density of states for some random operators with non-sign definite potentials,” J. Funct. Anal. 195, 1247 (2002).
http://dx.doi.org/10.1006/jfan.2002.3947
13.
13. Hupfer, T. , Leschke, H. , Müller, P. , and Warzel, S. , “The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials,” Commun. Math. Phys. 221(2), 229254 (2001).
http://dx.doi.org/10.1007/s002200100467
14.
14. Klopp, F. , Loss, M. , Nakamura, S. , and Stolz, G. , “Localization for the random displacement model,” Duke Math. J. 161(4), 587621 (2012);
http://dx.doi.org/10.1215/00127094-1548353
14.e-print arXiv:1007.2483v1.
15.
15. Klopp, F. , Nakamura, S. , Nakano, F. , and Nomura, Y. , “Anderson localization for 2D discrete Schrödinger operators with random magnetic fields,” Ann. Henri Poincaré 4, 795811 (2003).
http://dx.doi.org/10.1007/s00023-003-0147-3
16.
16. Nakamura, S. , “Lifshitz tail for 2D discrete Schrödinger operator with random magnetic field,” Ann. Henri Poincaré 1, 823835 (2000).
http://dx.doi.org/10.1007/PL00001016
17.
17. Ueki, N. , “Wegner estimates and localization for random magnetic fields,” Osaka J. Math. 45, 565608 (2008).
18.
18. Veselić, I. , “Wegner estimate and the density of states of some indefinite alloy-type Schrödinger operators,” Lett. Math. Phys. 59(3), 199214 (2002).
http://dx.doi.org/10.1023/A:1015580402816
19.
19. Wegner, F. , “Bounds on the density of states in disordered systems,” Z. Phys. B 44(1–2), 915 (1981).
http://dx.doi.org/10.1007/BF01292646
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/3/10.1063/1.4794082

/content/aip/journal/jmp/54/3/10.1063/1.4794082
2013-03-21
2013-12-09

/deliver/fulltext/aip/journal/jmp/54/3/1.4794082.html;jsessionid=2eid5yjeyt8x4.x-aip-live-03?itemId=/content/aip/journal/jmp/54/3/10.1063/1.4794082&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/jmp

Article
content/aip/journal/jmp
Journal
5
3

### Most cited this month

More Less
true
true
This is a required field