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- W2906703349 abstract "We prove that for $kappain(0,8)$, if $(eta_1,eta_2)$ is a $2$-SLE$_kappa$ pair in a simply connected domain $D$ with an analytic boundary point $z_0$, then $lim_{rto 0^+}r^{-alpha} mathbb{P}[mbox{dist}(z_0,eta_j)<r,j=1,2]$ converges to a positive number for some $alpha>0$, which is called the two-curve Green's function. The exponent $alpha$ equals $frac{12}{kappa}-1$ or $2(frac{12}{kappa}-1)$ depending on whether $z_0$ is one of the endpoints of $eta_1$ and $eta_2$. We also find the convergence rate and the exact formula of the Green's function up to a multiplicative constant. To derive these results, we construct two-dimensional diffusion processes and use orthogonal polynomials to obtain their transition density." @default.
- W2906703349 created "2019-01-11" @default.
- W2906703349 creator A5065127781 @default.
- W2906703349 date "2019-01-01" @default.
- W2906703349 modified "2023-09-23" @default.
- W2906703349 title "Two-curve Green's function for $2$-SLE: the boundary case" @default.
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- W2906703349 doi "https://doi.org/10.48550/arxiv.1901.00254" @default.
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