Commutation relations for Schramm-Loewner evolutions

Communications on Pure and Applied Mathematics

Volumn 60, Issue 12, 2007, Pages 1792-1847

  Dubédat, Julien ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36248999560     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20191     Document Type: Article

References (28)

1. Aizenman, M.; Burchard, A. Holder regularity and dimension bounds for random curves. Duke Math. J. 99 (1999), no. 3, 419-453.
2. Bauer, R. O.; Friedrich, R. M. On chordal and bilateral SLE in multiply connected domains. Preprint. arXiv:math.PR/0503178, 2005.
3. Beffara, V. The dimension of SLE curves. Preprint. arXiv:math.PR/0211322, 2002.
4. Camia, F.; Newman, C. M. The full scaling limit of two-dimensional critical percolation. Preprint. arXiv:math.PR/0504036, 2005.
5. Cardy, J. Stochastic Loewner evolution and Dyson's circular ensembles. J. Phys. A 36 (2003), no. 24, L379-L386.
6. Cardy, J. Corrigendum: "Stochastic Loewner evolution and Dyson's circular ensembles" [J. Phys. A 36 (2003), no. 24, L379-L386],
7. J. Phys. A 36 (2003), no. 49, 12343.
8. 6. Comm. Math. Phys. 245 (2004), no. 3, 627-637.
9. Dubédat, J. Excursion decompositions for SLE and Watts' crossing formula. Probab. Theory Related Fields 134 (2006), no. 3, 453-488.
10. Dubédat, J. Euler integrals for commuting SLEs. J. Stat. Phys. 123 (2006), no. 6, 1183-1218.
11. Dubédat, J. SLE(κ, ρ) martingales and duality. Ann. Probab. 33 (2005), no. 1, 223-243.
12. Fomin, S. Loop-erased walks and total positivity. Trans. Amer. Math. Soc. 353 (2001), no. 9, 3563-3583 (electronic).
13. Kozdron, M. J.; Lawler, G. F. Estimates of random walk exit probabilities and application to loop-erased random walk. Electron. J. Probab. 10 (2005), 1442-1467 (electronic).
14. Lawler, G.; Schramm, O.; Werner, W. Conformal restriction: the chordal case. J. Amer. Math. Soc. 16 (2003), no. 4, 917-955 (electronic).
15. Lawler, G. F. The Laplacian-b random walk and the Schramm-Loewner evolution. Illinois J. Math. 50 (2006), no. 1-4, 701-746 (electronic).
16. Lawler, G. F. Conformally invariant processes in the plane. Mathematical Surveys and Monographs, 114. American Mathematical Society, Providence, R.I., 2005.
17. Lawler, G. F.; Schramm, O.; Werner, W. Conformal invariance of planar loop-erased random walks and uniform spanning trees. Ann. Probab. 32 (2004), no. 1B, 939-995.
18. Lawler, G. F.; Werner, W. The Brownian loop soup. Probab. Theory Related Fields 128 (2004), no. 4, 565-588.
19. Rohde, S.; Schramm, O. Basic properties of SLE. Ann. of Math. (2) 161 (2005), no. 2, 883-924.
20. Schramm, O. Scaling limits of loop-erased random walks and uniform spanning trees. Israel J. Math. 118 (2000), 221-288.
21. Schramm, O. A percolation formula. Electron. Comm. Probab. 6 (2001), 115-120 (electronic).
22. Smirnov, S. 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.
23. Werner, W. Girsanov's transformation for SLE(κ, ρ) processes, intersection exponents and hiding exponents. Ann. Fac. Sci. Toulouse Math. (6) 13 (2004), no. 1, 121-147.
24. Werner, W. Random planar curves and Schramm-Loewner evolutions. Lectures on probability theory and statistics, 107-195. Lecture Notes in Math., 1840. Springer, Berlin, 2004.
25. Werner, W. Conformal restriction and related questions. Probab. Surv. 2 (2005), 145-190 (electronic).
26. Wilson, D. Generating random spanning trees more quickly than the cover time. Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996), 296-303. ACM, New York, 1996.
27. Zhan, D. Random Loewner chains in Riemann surfaces. Thesis. California Institute of Technology, Pasadena, Calif., 2004.
28. Zhan, D. Stochastic Loewner evolution in doubly connected domains. Probab. Theory Related Fields 129 (2004), no. 3, 340-380.