Girsanov’s transformation for \(\text{SLE}(\kappa,\rho)\) processes, intersection exponents and hiding exponents. (English) Zbl 1059.60099
Using the Schramm-Loewner evolution process SLE(\(\kappa , \rho \)), introduced by G. Lawler, O. Schramm and the author [J. Am. Math. Soc. 16, No. 4, 917–955 (2003; Zbl 1030.60096)], some new exponents, which describe probabilities of events associated to planar Brownian motions, are computed. This is done by relating the formulas giving Brownian intersection exponents to the absolute continuity relations between Bessel processes and SLE(\(\kappa , \rho \)). Such exponents are conjectured to be relevant in the study of the two-dimensional critical systems from statistical physics.
Reviewer: Liliana Popa (Iaşi)
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60J65 | Brownian motion |
| 82B27 | Critical phenomena in equilibrium statistical mechanics |
Citations:
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