Jacob Calvert
I am a PhD student at UC Berkeley working in the areas of probability and data science. Recently, I have been studying a class of random processes that exhibit a remarkable phase transition observed in natural collectives. To learn more, check out Papers or Posts.
Given finite $A \subset \mathbb{Z}^2$, the harmonic measure of $x \in A$ is the probability that a simple random walk “from infinity” first visits $A$ at $x$. If $A$ has $n$ elements, what is the smallest positive harmonic measure that you can get?
This post discusses the intersection of some of my recent and forthcoming work in probability theory with studies of programmable matter and ant colonies.