Jacob Calvert
I recently completed a PhD in probability theory at UC Berkeley. 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.
This post explains how the Markov chain dichotomy of transience and recurrence implies dichotomous behavior for certain models of collective motion.
This post highlights recent work which constitutes only the third rigorous result about planar diffusion-limited aggregation (DLA), a paradigmatic model of random, dendritic growth.
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?