Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Intersection and mixing times for reversible chains
(20170101) 
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 ...