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


  • Baratt K., Karmakar S.N. and Chakrabarti B.K.: Self-avoiding walk, connectivity constant and theta point on percolating lattices phJ. Phys. A Math. Gen. 24 (1991) 851-860.
  • Bertin P.: Free energy for Linear Stochastic Evolutions in dimension two, phpreprint (2009).
  • Bertin P.: Free energy for directed polymer in Brownian environment, phpreprint (2009).
  • Birkner, Matthias. A condition for weak disorder for directed polymers in random environment. Electron. Comm. Probab. 9 (2004), 22--25 (electronic). MR2041302
  • Blease J.: Directed bond percolation on hypercubic lattices, phJ. Phys. C. 10 (1977) 925--936.
  • Carmona, Philippe; Hu, Yueyun. On the partition function of a directed polymer in a Gaussian random environment. Probab. Theory Related Fields 124 (2002), no. 3, 431--457. MR1939654
  • Comets, Francis; Popov, Serguei; Vachkovskaia, Marina. The number of open paths in an oriented $\rho$-percolation model. J. Stat. Phys. 131 (2008), no. 2, 357--379. MR2386584
  • Comets, Francis; Vargas, Vincent. Majorizing multiplicative cascades for directed polymers in random media. ALEA Lat. Am. J. Probab. Math. Stat. 2 (2006), 267--277. MR2249671
  • Comets, Francis; Yoshida, Nobuo. Directed polymers in random environment are diffusive at weak disorder. Ann. Probab. 34 (2006), no. 5, 1746--1770. MR2271480
  • Cox, J. Theodore; Durrett, Richard. Oriented percolation in dimensions $d\geq 4$: bounds and asymptotic formulas. Math. Proc. Cambridge Philos. Soc. 93 (1983), no. 1, 151--162. MR0684285
  • Dammer S.M. and Haye H.: Spreading with immunization in high dimensions, phJ. Stat. Mech: Theory Exp. 7 (2004) P07011.
  • Darling, R. W. R. The Lyapunov exponent for products of infinite-dimensional random matrices. Lyapunov exponents (Oberwolfach, 1990), 206--215, Lecture Notes in Math., 1486, Springer, Berlin, 1991. MR1178959
  • Duminil-Copin H., Smirnov S.: The connective constant for the honeycomb equals sqrt2+sqrt 2 phAnn. of Math. 175 (2012) 1653-1665 ARXIV1007.0575.
  • Durrett, Richard; Perkins, Edwin A. Rescaled contact processes converge to super-Brownian motion in two or more dimensions. Probab. Theory Related Fields 114 (1999), no. 3, 309--399. MR1705115
  • Fukushima R. and Yoshida N.: On the exponential growth for a certain class of linear systems ARXIV1205.6559.
  • Hammersley, J. M. Bornes supérieures de la probabilité critique dans un processus de filtration. (French) 1959 Le calcul des probabilités et ses applications. Paris, 15-20 juillet 1958 pp. 17--37 Colloques Internationaux du Centre National de la Recherche Scientifique, LXXXVII Centre National de la Recherche Scientifique, Paris MR0105751
  • van der Hofstad, Remco; Slade, Gordon. Asymptotic expansions in $n^ {-1}$ for percolation critical values on the $n$-cube and $\Bbb Z^ n$. Random Structures Algorithms 27 (2005), no. 3, 331--357. MR2162602
  • van der Hofstad, Remco; Sakai, Akira. Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions. Probab. Theory Related Fields 132 (2005), no. 3, 438--470. MR2197108
  • Kesten, H.; Stigum, B. P. A limit theorem for multidimensional Galton-Watson processes. Ann. Math. Statist. 37 1966 1211--1223. MR0198552
  • Lacoin, Hubert. New bounds for the free energy of directed polymers in dimension $1+1$ and $1+2$. Comm. Math. Phys. 294 (2010), no. 2, 471--503. MR2579463
  • Lacoin, Hubert. Influence of spatial correlation for directed polymers. Ann. Probab. 39 (2011), no. 1, 139--175. MR2778799
  • Lacoin H.: On the two dimensional supercritical percolation cluster, the number of self-avoiding paths is much smaller than expected, ARXIV1203.6051.
  • Madras, Neal; Slade, Gordon. The self-avoiding walk. Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1993. xiv+425 pp. ISBN: 0-8176-3589-0 MR1197356
  • Lyons, Russell; Pemantle, Robin; Peres, Yuval. Conceptual proofs of $L\log L$ criteria for mean behavior of branching processes. Ann. Probab. 23 (1995), no. 3, 1125--1138. MR1349164
  • Slade, G. The lace expansion and its applications. Lectures from the 34th Summer School on Probability Theory held in Saint-Flour, July 6–24, 2004. Edited and with a foreword by Jean Picard. Lecture Notes in Mathematics, 1879. Springer-Verlag, Berlin, 2006. xiv+228 pp. ISBN: 978-3-540-31189-8; 3-540-31189-0 MR2239599
  • Yoshida, Nobuo. Phase transitions for the growth rate of linear stochastic evolutions. J. Stat. Phys. 133 (2008), no. 6, 1033--1058. MR2462010
  • Yoshida, Nobuo. Localization for linear stochastic evolutions. J. Stat. Phys. 138 (2010), no. 4-5, 598--618. MR2594914

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