论文信息 - Harmonic explorer and its convergence to SLE4

Harmonic explorer and its convergence to SLE4

The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE 4 as the grid gets finer.

Oded Schramm | Scott Sheffield | O. Schramm | S. Sheffield

[1] I. Benjamini,et al. Random walks and harmonic functions on infinite planar graphs using square tilings , 1996 .

[2] Oded Schramm,et al. Basic properties of SLE , 2001 .

[3] Zheng-Xu He,et al. Hyperbolic and parabolic packings , 1995, Discret. Comput. Geom..

[4] O. Schramm. Transboundary extremal length , 1995 .

[5] Wendelin Werner. Random planar curves and Schramm-Loewner evolutions , 2003 .

[6] Wendelin Werner,et al. Conformal invariance of planar loop-erased random walks and uniform spanning trees , 2001 .

[7] O. Schramm,et al. Conformal restriction: The chordal case , 2002, math/0209343.

[8] S. Smirnov. Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits , 2001 .

[9] C. Pommerenke. Boundary Behaviour of Conformal Maps , 1992 .

[10] Oded Schramm. A Percolation Formula , 2001 .

[11] Dudley,et al. Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .

[12] G. Lawler,et al. Universality for conformally invariant intersection exponents , 2000 .

[13] G. McCaughan. A recurrence/transience result for circle packings , 1998 .

[14] V. Kaimanovich. An introduction to the Stochastic Loewner Evolution , 2004 .

[15] José L. Fernández,et al. Quasilines and conformal mappings , 1981 .

[16] L. Ahlfors. Conformal Invariants: Topics in Geometric Function Theory , 1973 .