Diffusion in random media

• Applicant: Professor Dr. Peter Stollmann
• Subject Area: Mathematics
• Term: from 2003 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5401722

• Final Report Year: 2010

Final Report Abstract

No abstract available

Publications

• Bounds on the spectral shift function and the density of states. Comm. Math. Phys. 262 (2006), no. 2, 489-503
  Hundertmark, Dirk ; Killip, Rowan ; Nakamura, Shu ; Stollmann, Peter ; Veselic, Ivan
  
• Localization near fluctuation boundaries via fractional moments and applications. J. Anal. Math. 100 (2006), 83-116
  Boutet de Monvel, A. ; Naboko, S. ; Stollmann, P. ; Stolz, G.
  
• Linear Wegner estimate for alloy-type Schrödinger operators on metric graphs. J. Math. Phys. 48 (2007), no. 9, 092107, 7 pp
  Helm, Mario ; Veselic, Ivan
  
• Localization on a quantum graph with a random potential on the edges. Rev. Math. Phys. 19 (2007), no. 9, 923-939
  Exner, Pavel ; Helm, Mario ; Stollmann, Peter
  
• Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs. J. Funct. Anal. 252 (2007), no. 1, 233-246
  Müller, Peter ; Stollmann, Peter
  
• Eigenfunction expansions for Schrödinger operators on metric graphs. Integral Equations Operator Theory 62 (2008), no. 4, 541-553
  Lenz, Daniel ; Schubert, Carsten ; Stollmann, Peter
  
• Optimal Wegner estimates for random Schrödinger operators on metric graphs. Analysis on graphs and its applications, 409-422, Proc. Sympos. Pure Math., 77, Amer. Math. Soc, Providence, RI, 2008
  Gruber, Michael J. ; Helm, Mario ; Veselic, Ivan
  
• Sch'nors theorem for strongly local forms. Israel J. Math. 173 (2009), 189-211
  Boutet de Monvel, Anne ; Lenz, Daniel ; Stollmann, Peter
  
• From Uncertainty Principles to Wegner Estimates. Math. Phys. Anal. Geom. 2010
  Stollmann, Peter
  (See online at https://doi.org/10.1007/s11040-010-9072-0)
• Wegnertype Bounds for a Multi-particle Continuous Anderson Model with an Alloy-type External Potential. J. Stat. Phys. 138 (2010), 553-566
  A. Boutet de Monvel, V. Chulaevsky, P. Stollmann and Y. Suhov
  (See online at https://doi.org/10.1007/s10955-009-9883-1)