## Probability

•  Dapeng Zhan, MSU
•  Boundary Green's function and Minkowski content for SLE$_\kappa(\rho)$
•  10/26/2022
•  3:00 PM - 3:50 PM
•  C405 Wells Hall
•  Dapeng Zhan (zhan@msu.edu)

We prove the existence of the Minkowski content of the intersection of an SLE$_\kappa(\rho)$ curve with a real interval using the standard approach, which is to estimate the convergence rate of one-point and two-point boundary Green's functions of SLE$_\kappa(\rho)$. Then we show the existence of a conformally covariant measure called Minkowski content measure on the intersection of an SLE$_\kappa(\rho)$ curve with a half real line, which is closely related to the Minkowski content. Using the Minkowski content measure, we construct rooted and unrooted SLE$_\kappa(\rho)$ bubble measures, which are supported on loops and satisfy SLE$_\kappa(\rho)$-type domain Markov property.

## Contact

Department of Mathematics
Michigan State University
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College of Natural Science