## Probability

•  Parametrized SLE curves with self-similarity and stationary increments
•  09/21/2017
•  3:00 PM - 3:50 PM
•  C405 Wells Hall
•  Dapeng Zhan, MSU

We describe an SLE$_\kappa$ curve, $\kappa\in(0,8)$, which is parametrized by $(d:=1+\frac \kappa 8)$-dimensional Minkowski content, and has self-similarity of exponent $1/d$ and stationary increments. We then prove that such SLE$_\kappa$ curve is $\alpha$-H\"older continuous for any $\alpha<1/d$, and Mckean's dimension theorem holds for this curve.

## Contact

Department of Mathematics
Michigan State University