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

  • Antal, Peter; Pisztora, Agoston. On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996), no. 2, 1036--1048. MR1404543
  • Bandyopadhyay, Antar; Zeitouni, Ofer. Random walk in dynamic Markovian random environment. ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006), 205--224. MR2249655
  • Barlow, Martin T.; Černý, Jiří. Convergence to fractional kinetics for random walks associated with unbounded conductances. Probab. Theory Related Fields 149 (2011), no. 3-4, 639--673. MR2776627
  • Berger, N.; Biskup, M.; Hoffman, C. E.; Kozma, G. Anomalous heat-kernel decay for random walk among bounded random conductances. Ann. Inst. Henri Poincaré Probab. Stat. 44 (2008), no. 2, 374--392. MR2446329
  • M. Biskup and O. Boukhadra. Subdiffusive heat kernel decay in four-dimensional iid random conductance models. ARXIV1010.5542v1 %arXiv:1010.5542v1 (2010).
  • Boldrighini, C.; Minlos, R. A.; Pellegrinotti, A. Almost-sure central limit theorem for a Markov model of random walk in dynamical random environment. Probab. Theory Related Fields 109 (1997), no. 2, 245--273. MR1477651
  • Boukhadra, Omar. Heat-kernel estimates for random walk among random conductances with heavy tail. Stochastic Process. Appl. 120 (2010), no. 2, 182--194. MR2576886
  • Boukhadra, Omar. Standard spectral dimension for the polynomial lower tail random conductances model. Electron. J. Probab. 15 (2010), no. 68, 2069--2086. MR2745726
  • S. Buckley. Problems in Random Walks in Random Environments. DPhil thesis, University of Oxford (2011).
  • Coulhon, Thierry; Grigorʹyan, Alexander; Zucca, Fabio. The discrete integral maximum principle and its applications. Tohoku Math. J. (2) 57 (2005), no. 4, 559--587. MR2203547
  • Delmotte, Thierry. Parabolic Harnack inequality and estimates of Markov chains on graphs. Rev. Mat. Iberoamericana 15 (1999), no. 1, 181--232. MR1681641
  • Giacomin, Giambattista; Olla, Stefano; Spohn, Herbert. Equilibrium fluctuations for $\nabla\phi$ interface model. Ann. Probab. 29 (2001), no. 3, 1138--1172. MR1872740
  • Grimmett, Geoffrey. Percolation. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 321. Springer-Verlag, Berlin, 1999. xiv+444 pp. ISBN: 3-540-64902-6 MR1707339
  • Mathieu, Pierre; Remy, Elisabeth. Isoperimetry and heat kernel decay on percolation clusters. Ann. Probab. 32 (2004), no. 1A, 100--128. MR2040777
  • Pang, M. M. H. Heat kernels of graphs. J. London Math. Soc. (2) 47 (1993), no. 1, 50--64. MR1200977
  • Rassoul-Agha, Firas; Seppäläinen, Timo. An almost sure invariance principle for random walks in a space-time random environment. Probab. Theory Related Fields 133 (2005), no. 3, 299--314. MR2198014
  • Saloff-Coste, L.; Zúñiga, J. Merging for time inhomogeneous finite Markov chains. I. Singular values and stability. Electron. J. Probab. 14 (2009), 1456--1494. MR2519527
  • Saloff-Coste, L.; Zúñiga, J. Merging for inhomogeneous finite Markov chains, Part II: Nash and log-Sobolev inequalities. Ann. Probab. 39 (2011), no. 3, 1161--1203. MR2789587
  • Sidoravicius, Vladas; Sznitman, Alain-Sol. Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Related Fields 129 (2004), no. 2, 219--244. MR2063376
Bookmark and Share


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