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


  • Adler, Robert J. An introduction to continuity, extrema, and related topics for general Gaussian processes. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 12. Institute of Mathematical Statistics, Hayward, CA, 1990. x+160 pp. ISBN: 0-940600-17-X MR1088478
  • Barlow, Martin T.; Bass, Richard F. The construction of Brownian motion on the Sierpiński carpet. Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), no. 3, 225--257. MR1023950
  • Barlow, Martin T.; Bass, Richard F. Random walks on graphical Sierpinski carpets. Random walks and discrete potential theory (Cortona, 1997), 26--55, Sympos. Math., XXXIX, Cambridge Univ. Press, Cambridge, 1999. MR1802425
  • Barlow, Martin T.; Bass, Richard F. Brownian motion and harmonic analysis on Sierpinski carpets. Canad. J. Math. 51 (1999), no. 4, 673--744. MR1701339
  • Barlow, Martin T.; Coulhon, Thierry; Kumagai, Takashi. Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs. Comm. Pure Appl. Math. 58 (2005), no. 12, 1642--1677. MR2177164
  • Barlow, M. T.; Hambly, B. M. Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets. Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), no. 5, 531--557. MR1473565
  • Bramson, Maury; Zeitouni, Ofer. Tightness for a family of recursion equations. Ann. Probab. 37 (2009), no. 2, 615--653. MR2510018
  • Bramson, Maury; Zeitouni, Ofer. Tightness of the recentered maximum of the two-dimensional discrete Gaussian free field. Comm. Pure Appl. Math. 65 (2012), no. 1, 1--20. MR2846636
  • S. Chatterjee. Chaos, concentration, and multiple valleys. Preprint 2008. arXiv:0810.4221
  • Ding, Jian; Lee, James R.; Peres, Yuval. Cover times, blanket times, and majorizing measures. Ann. of Math. (2) 175 (2012), no. 3, 1409--1471. MR2912708
  • Eisenbaum, Nathalie; Kaspi, Haya; Marcus, Michael B.; Rosen, Jay; Shi, Zhan. A Ray-Knight theorem for symmetric Markov processes. Ann. Probab. 28 (2000), no. 4, 1781--1796. MR1813843
  • Grigor'yan, Alexander; Telcs, Andras. Two-sided estimates of heat kernels on metric measure spaces. Ann. Probab. 40 (2012), no. 3, 1212--1284. MR2962091
  • Hambly, Ben M.; Kumagai, Takashi. Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries. Fractal geometry and applications: a jubilee of Benoît Mandelbrot, Part 2, 233--259, Proc. Sympos. Pure Math., 72, Part 2, Amer. Math. Soc., Providence, RI, 2004. MR2112125
  • Hambly, Ben M.; Kumagai, Takashi; Kusuoka, Shigeo; Zhou, Xian Yin. Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets. J. Math. Soc. Japan 52 (2000), no. 2, 373--408. MR1742797
  • Kigami, Jun. Resistance forms, quasisymmetric maps and heat kernel estimates. Mem. Amer. Math. Soc. 216 (2012), no. 1015, vi+132 pp. ISBN: 978-0-8218-5299-6 MR2919892
  • T. Kumagai. Random walks on disordered media and their scaling limits. St. Flour Lecture Notes (2010), to appear Lecture Notes in Mathematics, Springer. Current version available at
  • Kumagai, Takashi. Estimates of transition densities for Brownian motion on nested fractals. Probab. Theory Related Fields 96 (1993), no. 2, 205--224. MR1227032
  • Kusuoka, Shigeo; Yin, Zhou Xian. Dirichlet forms on fractals: Poincaré constant and resistance. Probab. Theory Related Fields 93 (1992), no. 2, 169--196. MR1176724
  • Ledoux, Michel; Talagrand, Michel. Probability in Banach spaces. Isoperimetry and processes. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 23. Springer-Verlag, Berlin, 1991. xii+480 pp. ISBN: 3-540-52013-9 MR1102015
  • R. Lyons and Y. Peres. Probability on Trees and Networks. Cambridge University Press. In preparation. Current version available at
  • Sheffield, Scott. Gaussian free fields for mathematicians. Probab. Theory Related Fields 139 (2007), no. 3-4, 521--541. MR2322706

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