Poisson Splitting by Factors (2009)
Holroyd, Alexander E., Lyons, Russell, Soo, Terry
Given a homogeneous Poisson process on R^d with intensity L, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an...
A Non-Measurable Set From Coin-Flips (2006)
Holroyd, Alexander E., Soo, Terry
In this expository note, we construct a non-measurable set in the probability space of coin flips indexed by the integers.
Translation-Invariant Matchings of Coin-Flips on Z^d (2006)
Consider independent fair coin flips at each site of the lattice Z^d. We study non-randomized translation-invariant perfect matching rules of occupied sites to unoccupied sites and determine bounds...
Mixing for Markov Chains and Spin Systems (2005)
Yuval Peres, Ra Kliem, Lionel Levine, Yun Long, Asaf Nachmias, Alex Skorokhod, ...
for help preparing these notes. These notes have not been subjected to the usual scrutiny reserved for formal publications. –Yuval Lecture 1: Introduction and total variation distance