### Recent Submissions

(2017-01-01)
• #### Chordal SLE$_6$ explorations of a quantum disk ﻿

We consider a particular type of $\sqrt{8/3}$-Liouville quantum gravity surface called a doubly marked quantum disk (equivalently, a Brownian disk) decorated by an independent chordal SLE$_6$ curve $\eta$ between its marked ...
• #### Capacity of the range of random walk on Z^d ﻿

We study the capacity of the range of a transient simple random walk on Z^d. Our main result is a central limit theorem for the capacity of the range for d \geq 6. We present a few open questions in lower dimensions.
• #### Strong law of large numbers for the capacity of the Wiener sausage in dimension four ﻿

We prove a strong law of large numbers for the Newtonian capacity of a Wiener sausage in the critical dimension four, where a logarithmic correction appears in the scaling. The main step of the proof is to obtain precise ...