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References
- Auer, P. Some hitting probabilities of random walks on Z2. In Limit Theorems in Probability and Statistics, volume 57 of Colloquia Mathematica Societatis János Bolyai, North-Holland, Budapest, Hungary, 1990. MR1116776
- Bass, R.F. Probabilistic Techniques in Analysis. Springer-Verlag, New York, NY, 1995. MR1329542
- Duren, P.L. Univalent functions, volume 259 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, New York, NY, 1983. MR0708494
- Fomin, S. Loop-erased walks and total positivity. Trans. Amer. Math. Soc. 353 (2001), 3563-3583. MR1837248
- Fukai, Y. and Uchiyama, K. Potential kernel for two-dimensional random walk. Ann. Probab. 24 (1996), 1979-1992. MR1415236
- Kenyon, R. The asymptotic determinant of the discrete Laplacian. Acta Math. 185 (2000), 239-286. MR1819995
- Komlós, J., Major, P., and Tusnády, G. An approximation of partial sums of independent RV'-s, and the sample DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32 (1975), 111-131. MR0375412
- Komlós, J., Major, P., and Tusnády, G. An approximation of partial sums of independent RV's, and the sample DF. II. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 34 (1976), 33-58. MR0402883
- Kozdron, M.J. Simple random walk excursion measure in the plane. Ph.D. dissertation, Duke University, Durham, NC, 2004. Math. Review number not available.
- Kozdron, M.J. On the scaling limit of simple random walk excursion measure in the plane. Preprint, 2005. Available online at arXiv:math.PR/0506337. Math. Review number not available.
- Lawler, G.F. Intersections of Random Walks. Birkhäuser, Boston, MA, 1991. MR1117680
- Lawler, G.F. Loop-erased random walk. In Perplexing Problems in Probability: Festschrift in Honor of Harry Kesten, volume 44 of Progress in Probability, 197-217. Birkhäuser, Boston, MA, 1999. MR1703133
- Lawler, G.F. Conformally Invariant Processes in the Plane, volume 114 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2005. MR2129588
- Lawler, G.F., Schramm, O., and Werner, W. Conformal invariance of planar loop-erased random walks and uniform spanning trees. Ann. Probab. 32 (2004), 939-995. MR2044671
- Schramm, O. and Sheffield, S. The harmonic explorer and its convergence to SLE(4). Preprint, 2003. Available online at arXiv:math.PR/0310210. Math. Review number not available.
- Smirnov, S. Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), 239-244. MR1851632
- Zhan, D. Stochastic Loewner evolution in doubly connected domains. Probab. Theory Related Fields 129 (2004), 340-380. MR2128237

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