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Jacob Calvert

I use probability theory to understand what collectives can or could do. My aim is to enable new functionality for engineered collectives, like robot swarms and smart materials, and generate novel scientific hypotheses about natural collectives, like groups of animals and biological tissues. To learn more, check out Papers or Posts.


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?

Numerosity-driven phase transitions

This post discusses the intersection of some of my recent and forthcoming work in probability theory with studies of programmable matter and ant colonies.