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Issue 3
May  2012
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LIANG Jing, LAN Shi-yi. Right-passage probabilities of $\emph{\textbf{SLE}}_{\bm {\kappa}}$ and critical percolation[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 24-29.
Citation: LIANG Jing, LAN Shi-yi. Right-passage probabilities of $\emph{\textbf{SLE}}_{\bm {\kappa}}$ and critical percolation[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 24-29.

Right-passage probabilities of $\emph{\textbf{SLE}}_{\bm {\kappa}}$ and critical percolation

  • Received Date: 2011-05-01
  • Rev Recd Date: 2011-08-01
  • Publish Date: 2012-05-25
  • This paper derived the probability formula for a chordal $SLE_{\kappa}$ trace across a given point in upper half plane $\mathbb{H}$. And on the basis of the left-passage probability, established the probability formula for a critical percolation in a closed unit circle without a given point. Finally, according to the relationship of exploration process and $SLE_{6}$, got that with the same starting and ending point, the trace of $SLE_{6}$ has the same distribution of self-avoiding walk.
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  • [1]
    {1}SMIRMOV S. Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits[J]. C R Acad Sci Paris

    s$\acute{e}$r Math, 2001, 333: 239-244.
    {2}LAWLER G F, SCHRAMM O, WERNER W. Values of Brownian intersection

    exponents $\mathbb{I}$: Half plane exponents[J]. Acta Math, 2001,

    187: 237-273.
    {3}WATTS G M T. A crossing probability for critical percolation in two

    dimensions[J]. J Phy A, 1996, 29(14): L363-L368.
    {4}SCHRAMM O. A percolation formula[J]. Electron Comm Probab, 2006, 6:

    115-120.
    {5}ROHDE S, SCHRAMM O. Basic properties of SLE[J]. Annals Math, 2005,

    161: 879-920.
    {6}GRUMMETT G. Percolation[M]. 2nd ed. Berlin: Springer-Verlag, 1999.
    {7}ERE$\acute{E}$LYI A, MAGNUS W, OBERHETTINGER F, et al. Higher

    transcendental functions[M]. New York: McGraw-Hill, 1953.
    {8}OBERHETTINGER F. Hypergeometric functions[M]// Handbook of

    Mathematics Functions with Formulas, Graphs, and Mathematical

    Tables. 10th ed. New York: Wiley, 1972: 555-566.
    {9}LAWLER G F, WERNER W. Universality for conformally invariant

    intersection exponents[J]. J Eur Math Soc, 2000, 2(4): 291-328.
    {10}SCHRAMM O. Scaling limit of loop-erased random walks and uniform

    spanning trees[J]. Israel J Math, 2000, 118: 221-288.
    {11}AIZENMAN M, BURCHARD A. H$\ddot{o}$lder regularity and dimension

    bounds for random curves[J]. Duke Math, 1999, 99(3): 419-453.
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