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.

A dichotomy in models of collective motion

This post explains how the Markov chain dichotomy of transience and recurrence implies dichotomous behavior for certain models of collective motion.

A third rigorous result about DLA

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.

A conjecture about harmonic measure

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?