## Discrete Mathematics and Statistical Mechanics

# Minkowski Content for Brownian cut points

## Xinyi Li (University of Chicago)

### Thursday, March 8, 2018
2:30 pm

MONT 214

Consider 2 or 3-dimensional Brownian motion and the set of its cut points. In this talk, we will discuss about its relationship with the intersection exponent and prove the existence of its Minkowski content as a random Borel measure. If time permits, I will also explain how we identify the Minkowski content with the scaling limit of the counting measure of pivotal points for percolation on the triangular lattice in the 2-dimensional case. This is a joint project with Nina Holden, Greg Lawler and Xin Sun.