The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Antal, Peter. Enlargement of obstacles for the simple random walk. Ann. Probab. 23 (1995), no. 3, 1061--1101. MR1349162 (96m:60158)
  2. Biskup, Marek; König, Wolfgang. Long-time tails in the parabolic Anderson model with bounded potential. Ann. Probab. 29 (2001), no. 2, 636--682. MR1849173 (2002j:60038)
  3. Carmona, René; Lacroix, Jean. Spectral theory of random Schrödinger operators. Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1990. xxvi+587 pp. ISBN: 0-8176-3486-X MR1102675 (92k:47143)
  4. den Hollander, Frank; Weiss, George H. Aspects of Trapping in Transport Processes. In Contemporary Problems in Statistical Physics, 147--203. Society for Industrial and Applied Mathematics, 1994. Math. Review number not available.
  5. Donsker, M. D.; Varadhan, S. R. S. Asymptotics for the Wiener sausage. Comm. Pure Appl. Math. 28 (1975), no. 4, 525--565. MR0397901 (53 #1757a)
  6. Fukushima, Masatoshi. On the spectral distribution of a disordered system and the range of a random walk. Osaka J. Math. 11 (1974), 73--85. MR0353462 (50 #5945)
  7. Fukushima, Ryoki. Brownian survival and Lifshitz tail in perturbed lattice disorder. J. Funct. Anal. 256 (2009), no. 9, 2867--2893. MR2502426
  8. Fukushima, Ryoki; Ueki, Naomasa. Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice. Kyoto University Preprint Series, Kyoto-Math 2009-10, submitted, 2009. Math. Review number not available.
  9. Havlin, Shlomo; Ben-Avraham, Daniel. Diffusion in disordered media. Adv. Phys., 36(6):695--798, 1987. Math. Review number not available.
  10. Kasahara, Yuji. Tauberian theorems of exponential type. J. Math. Kyoto Univ. 18 (1978), no. 2, 209--219. MR0501841 (80g:40008)
  11. Lifshitz, I. M. Energy spectrum structure and quantum states of disordered condensed systems. Uspehi Fiz. Nauk 83 617--663 (Russian); translated as Soviet Physics Uspekhi 7 1965 549--573. MR0181368 (31 #5597)
  12. Nakao, Shintaro. On the spectral distribution of the Schrödinger operator with random potential. Japan. J. Math. (N.S.) 3 (1977), no. 1, 111--139. MR0651925 (58 #31419)
  13. Pastur, L. A. The behavior of certain Wiener integrals as $t \rightarrow \infty$ and the density of states of Schrödinger equations with random potential. (Russian) Teoret. Mat. Fiz. 32 (1977), no. 1, 88--95. MR0449356 (56 #7661)
  14. Reed, Michael; Simon, Barry. Methods of modern mathematical physics. I. Functional analysis. Second edition. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. xv+400 pp. ISBN: 0-12-585050-6 MR0751959 (85e:46002)
  15. Romerio, M.; Wreszinski, W. On the Lifschitz singularity and the tailing in the density of states for random lattice systems. J. Statist. Phys. 21 (1979), no. 2, 169--179. MR0541078 (80h:82008)
  16. Seneta, Eugene. Regularly varying functions. Lecture Notes in Mathematics, Vol. 508. Springer-Verlag, Berlin-New York, 1976. v+112 pp. MR0453936 (56 #12189)
  17. Simon, Barry. Schrödinger semigroups. Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 3, 447--526. MR0670130 (86b:81001a)
  18. Sznitman, Alain-Sol. Brownian asymptotics in a Poissonian environment. Probab. Theory Related Fields 95 (1993), no. 2, 155--174. MR1214085 (94c:60173)
  19. Sznitman, Alain-Sol. Brownian motion, obstacles and random media. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 1998. xvi+353 pp. ISBN: 3-540-64554-3 MR1717054 (2001h:60147)
  20. van den Berg, M. A Gaussian lower bound for the Dirichlet heat kernel. Bull. London Math. Soc. 24 (1992), no. 5, 475--477. MR1173944 (93k:35116)


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.