Reflected planar Brownian motions, intertwining relations and crossing probabilities

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 40, Issue 5, 2004, Pages 539-552

  Dubédat, Julien ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Critical percolation; Intertwining relations; Reflected Brownian motion; Watts' formula

Indexed keywords

EID: 4444379389     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2003.11.005     Document Type: Article

References (20)

1. Abramowitz M. Stegun I. (Eds.) Handbook of Mathematical Functions 1965
2. Ahlfors L. Complex Analysis third ed. 1979 McGraw-Hill
3. Bateman H. Higher Transcendental Functions 1953 McGraw-Hill
4. Biane P. Quelques propriétés du mouvement brownien dans un cône Stochastic Process. Appl. 53 2 1994 233-240
5. Biane P. Intertwining of Markov semi-groups, some examples Séminaire de Probabilités, XXIX Lecture Notes in Math. vol. 1613 1995 30-36 Springer Berlin
6. Cardy J.L. Critical percolation in finite geometries J. Phys. A: Math. Gen. 25 1992 201-206
7. Carmona P. Petit F. Yor M. Beta-gamma random variables and intertwining relations between certain Markov processes Rev. Mat. Iberoamericana 14 2 1998 311-367
8. Kesten H. Percolation Theory for Mathematicians 1982 Birkhaüser
9. Lawler G. Schramm O. Werner W. Values of Brownian intersection exponents. I. Half-plane exponents Acta Math. 187 2 2001 237-273
10. Lawler G. Schramm O. Werner W. Conformal restriction: the chordal case J. Amer. Math. Soc. 16 2003 917-955
11. Le Gall J.F. Mouvement brownien, cônes et processus stables Probab. Theory Related Fields 76 1987 587-627
12. Le Gall J.F. Une approche élémentaire des théorèmes de décomposition de Williams Séminaire de Probabilités, XX, 1984/1985 Lecture Notes in Math. vol. 1204 1986 447-464 Springer Berlin
13. Revuz D. Yor M. Continuous Martingales and Brownian Motion 1991 Springer Berlin
14. Rogers L.C.G. Pitman J. Markov functions Ann. Probab. 9 1981 573-582
15. Rogers L.C.G. Williams D. Diffusions, Markov Processes, and Martingales. Volume One: Foundations second ed. 1993 Wiley
16. S. Smirnov, Critical percolation in the plane. I. Conformal Invariance and Cardy's formula II. Continuum scaling limit, 2001, in preparation
17. Varadhan S.R.S. Williams R.J. Brownian motion in a wedge with oblique reflection Comm. Pure Appl. Math. 38 1985 405-443
18. Virág B. Brownian beads Probab. Theory Related Fields 127 3 2003 367-387
19. Watts G.M.T. A crossing probability for critical percolation in two dimensions J. Phys. A: Math. Gen. 29 1996 363-368
20. Werner W. Critical exponents, conformal invariance and planar Brownian motion Proceedings of the 3rd Europ. Congress Math. Prog. Math. vol. 202 2001 87-103 Birkhäuser