Excursion decompositions for SLE and Watts' crossing formula

Probability Theory and Related Fields

Volumn 134, Issue 3, 2006, Pages 453-488

  Dubédat, Julien ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547188786     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-005-0446-3     Document Type: Article

References (31)

1. 6. Ann. Probab. 32 (3B), 2606-2629 (2004)
2. Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Phys. B, 241 (2), 333-380 (1984)
3. Bertoin, J.: Complements on the Hilbert transform and the fractional derivative of Brownian local times. J. Math. Kyoto Univ. 30 (4), 651-670 (1990)
4. 0(d) and its drift term (0
5. Cardy, J.L.: Critical percolation in finite geometries. J. Phys. A 25 (4), L201-L206 (1992)
6. Cardy, J.L.: Conformal invariance and percolation. preprint, arXiv:math-ph/0103018, 2001
7. Cardy, J.L.: Crossing formulae for critical percolation in an annulus. J. Phys. A 35 (41), L565-L572, (2002)
8. Carmona, P., Petit, F., Yor, M.: Beta-gamma random variables and intertwining relations between certain Markov processes. Rev. Mat. Iberoamericana 14 (2), 311-367 (1998)
9. Dubédat, J.: Reflected brownian motions, intertwining relations and crossing probabilities. Ann. Inst. H. Poincaré Probab. Statist. to appear, 2003
10. Dubédat, J.: SLE(κ,ρ) martingales and duality. Ann. Probab. to appear, 2003
11. 6. Comm. Math. Phys. 245 (3), 627-637 (2004)
12. Grimmett, G.: Percolation, volume 321 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, second edition, 1999
13. Itô, K., McKean, H.P. Jr.: Diffusion processes and their sample paths. Springer-Verlag, Berlin, 1974. Second printing, corrected, Die Grundlehren der mathematischen Wissenschaften, Band 125
14. Kleban, P., Zagier, D.: Crossing probabilities and modular forms. J. Statist. Phys. 113 (3-4), 431-454 (2003)
15. Langlands, R., Pouliot, P., Saint-Aubin, Y.: Conformal invariance in two-dimensional percolation. Bull. Amer. Math. Soc. (N.S.) 30 (1), 1-61 (1994)
16. Lawler, G, Schramm, O., Werner, W.: Conformal restriction: the chordal case. J. Amer. Math. Soc. 16 (4), 917-955 (electronic), (2003)
17. Lawler, G.F., Schramm, O., Werner, W.: Values of Brownian intersection exponents. III. Two-sided exponents. Ann. Inst. H. Poincaré Probab. Statist. 38 (1), 109-123 (2002)
18. Lawler, G.F., Schramm, O., Werner, W.: Conformal invariance of planar loop-erased random walks and uniform spanning trees. Ann. Probab. 32 (1B), 939-995 (2004)
19. Maier, R.S.: On crossing event formulas in critical two-dimensional percolation. J. Statist. Phys. 111 (5-6), 1027-1048 (2003)
20. Pinson, H.T.: Critical percolation on the torus. J. Statist. Phys. 75 (5-6), 1167-1177 (1994)
21. Pitman, J., Yor, M.: A decomposition of Bessel bridges. Z. Wahrsch. Verw. Gebiete 59 (4), 425-457 (1982)
22. Revuz, D., Yor, M.: Continuous martingales and Brownian motion. Volume 293 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, third edition, 1999
23. Rogers, L.C.G., Williams, D.: Diffusions, Markov processes, and martingales. Vol. 1. John Wiley & Sons Ltd., Chichester, second edition, 1994
24. Rohde, S., Schramm, O.: Basic Properties of SLE. Ann. Math. to appear, 2001
25. Schramm, O.: Scaling limits of loop-erased random walks and uniform spanning trees. Israel J. Math. 118, 221-288 (2000)
26. Smirnov, S.: Critical percolation in the plane. I. Conformal Invariance and Cardy's formula II. Continuum scaling limit. in preparation, 2001
27. Taylor, S.J., Wendel, J.G.: The exact Hausdorff measure of the zero set of a stable process. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 6, 170-180 (1966)
28. Virág, B.: Brownian beads. Probab. Theory Relat. Fields 127 (3), 367-387 (2003)
29. Watts, G.M.T.: A crossing probability for critical percolation in two dimensions. J. Phys. A 29 (14), L363-L368 (1996)
30. Werner, W.: Girsanov's transformation for SLE(κ,ρ) processes, intersection exponents and hiding exponents. Ann. Fac. Sci. Toulouse Math. (6) 13 (1), 121-147 (2004)
31. Werner, W.: Lectures on random planar curves and Schramm-Loewner evolution. In: Lecture Notes of the 2002 St-Flour summer school, number 1840 in Lecture Notes in Math., Springer-Verlag, 2004, pp. 107-195