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  • Ahlfors, Lars V. Conformal invariants: topics in geometric function theory. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. ix+157 pp. MR0357743
  • M. Aizenman, B. Duplantier, A. Aharony (1999), Path crossing exponents and the external perimeter in 2D percolation. Phys. Rev. Let. 83, 1359--1362.
  • Cardy, John L. Critical percolation in finite geometries. J. Phys. A 25 (1992), no. 4, L201--L206. MR1151081
  • P. Grassberger (1999), Conductivity exponent and backbone dimension in 2-d percolation, Physica A 262, 251.
  • Grimmett, Geoffrey. Percolation. Springer-Verlag, New York, 1989. xii+296 pp. ISBN: 0-387-96843-1 MR0995460
  • Kesten, Harry. Percolation theory for mathematicians. Progress in Probability and Statistics, 2. Birkhäuser, Boston, Mass., 1982. iv+423 pp. ISBN: 3-7643-3107-0 MR0692943
  • Kesten, Harry. Scaling relations for $2$D-percolation. Comm. Math. Phys. 109 (1987), no. 1, 109--156. MR0879034
  • Kesten, H.; Sidoravicius, V.; Zhang, Y. Almost all words are seen in critical site percolation on the triangular lattice. Electron. J. Probab. 3 (1998), no. 10, 75 pp. (electronic). MR1637089
  • Lawler, Gregory F. Intersections of random walks. Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1991. 219 pp. ISBN: 0-8176-3557-2 MR1117680
  • Lawler, Gregory F. Loop-erased random walk. Perplexing problems in probability, 197--217, Progr. Probab., 44, Birkhäuser Boston, Boston, MA, 1999. MR1703133
  • Lawler, Gregory F. An introduction to the stochastic Loewner evolution. Random walks and geometry, 261--293, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. MR2087784
  • Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin. Values of Brownian intersection exponents. I. Half-plane exponents. Acta Math. 187 (2001), no. 2, 237--273. MR1879850
  • Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin. Values of Brownian intersection exponents. II. Plane exponents. Acta Math. 187 (2001), no. 2, 275--308. MR1879851
  • Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin. Values of Brownian intersection exponents. III. Two-sided exponents. Ann. Inst. H. Poincaré Probab. Statist. 38 (2002), no. 1, 109--123. MR1899232
  • Nienhuis, Bernard. Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas. J. Statist. Phys. 34 (1984), no. 5-6, 731--761. MR0751711
  • Nienhuis, B.; Riedel, E. K.; Schick, M. Variational renormalisation-group approach to the $q$-state Potts model in two dimensions. J. Phys. A 13 (1980), no. 2, L31--L34. MR0558635
  • M.P.M. den Nijs (1979), A relation between the temperature exponents of the eight-vertex and the q-state Potts model, J. Phys. A 12, 1857--1868.
  • Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1994. xii+560 pp. ISBN: 3-540-57622-3 MR1303781
  • Rohde, Steffen; Schramm, Oded. Basic properties of SLE. Ann. of Math. (2) 161 (2005), no. 2, 883--924. MR2153402
  • Schramm, Oded. Scaling limits of loop-erased random walks and uniform spanning trees. Israel J. Math. 118 (2000), 221--288. MR1776084
  • Schramm, Oded. A percolation formula. Electron. Comm. Probab. 6 (2001), 115--120 (electronic). MR1871700
  • Smirnov, Stanislav. Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), no. 3, 239--244. MR1851632
  • S. Smirnov (2001), in preparation.
  • Smirnov, Stanislav; Werner, Wendelin. Critical exponents for two-dimensional percolation. Math. Res. Lett. 8 (2001), no. 5-6, 729--744. MR1879816

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