NDLI: Ergodicity of the tip of an SLE curve

Content Provider	Springer Nature Link
Author	Zhan, Dapeng
Copyright Year	2015
Abstract	We first prove that, for $$\kappa \in (0,4)$$ , a whole-plane $$\hbox {SLE}(\kappa ;\kappa +2)$$ trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for $$\kappa \in (0,4)$$ , a chordal $$\hbox {SLE}_\kappa $$ curve stopped at a fixed capacity time can be mapped conformally to the initial segment of a whole-plane $$\hbox {SLE}(\kappa ;\kappa +2)$$ trace. A similar but weaker result holds for radial $$\hbox {SLE}_\kappa $$ . These results are then used to study the ergodic behavior of an SLE curve near its tip point at a fixed capacity time. The proofs rely on the symmetry of backward SLE weldings and conformal removability of $$\hbox {SLE}_\kappa $$ curves for $$\kappa \in (0,4)$$ .
Ending Page	360
Page Count	28
Starting Page	333
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	1
Volume Number	164
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-01-07
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical and Computational Biology Statistics for Business/Economics/Mathematical Finance/Insurance Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Operation Research/Decision Theory Quantitative Finance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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