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2021 Two-curve Green’s function for 2-SLE: the boundary case
Dapeng Zhan
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Electron. J. Probab. 26: 1-58 (2021). DOI: 10.1214/21-EJP592

Abstract

We prove that for κ(0,8), if (η1,η2) is a 2-SLEκpair in a simply connected domain D with an analytic boundary point z0, then as r0+, P[dist(z0,ηj)<r,j=1,2] converges to a positive number for some α>0, which is called the two-curve Green’s function. The exponent α equals 12κ1 or 2(12κ1) depending on whether z0 is one of the endpoints of η1 or η2. We also find the convergence rate and the exact formula for 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.

Citation

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Dapeng Zhan. "Two-curve Green’s function for 2-SLE: the boundary case." Electron. J. Probab. 26 1 - 58, 2021. https://doi.org/10.1214/21-EJP592

Information

Received: 22 June 2020; Accepted: 30 January 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-EJP592

Subjects:
Primary: 30C, 60G

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Vol.26 • 2021
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