Abstract
We prove that, for κ∈(0,4) and ρ≥(κ−4)/2, the chordal SLE(κ;ρ) trace started from (0;0+) or (0;0−) satisfies the reversibility property. And we obtain the equation for the reversal of the chordal SLE(κ;ρ) trace started from (0;b 0), where b 0>0.
Similar content being viewed by others
References
Dubédat, J.: SLE(κ,ρ) martingales and duality. Ann. Probab. 33(1), 223–243 (2005)
Dubédat, J.: Duality of Schramm-Loewner evolutions, arXiv:0711.1884
Lawler, G.F., Schramm, O., Werner, W.: Conformal restriction: The chordal case. J. Am. Math. Soc. 16(4), 917–955 (2003)
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)
Schramm, O., Sheffield, S.: Contour lines of the two-dimensional discrete Gaussian free field. Acta Math. 202(1), 21–137 (2009)
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards Applied Mathematics, Washington (1964)
Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion. Springer-Verlag, Berlin (1991)
Rohde, S., Schramm, O.: Basic properties of SLE. Ann. Math. 161(2), 883–924 (2005)
Zhan, D.: Reversibility of chordal SLE. Ann. Probab. 36(4), 1472–1494 (2008)
Zhan, D.: Duality of chordal SLE. Inven. Math. 174(2), 309–353 (2008)
Zhan, D.: Duality of chordal SLE, II. Ann. Inst. Henri Poincaré (in press)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhan, D. Reversibility of Some Chordal SLE(κ;ρ) Traces. J Stat Phys 139, 1013–1032 (2010). https://doi.org/10.1007/s10955-010-9978-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-010-9978-8