DMS Analysis and Stochastic Analysis Seminar (SASA)

Speaker: Alexander Dunlap (Duke University)

Title: Branching Brownian motion, voting models, and nonlocal PDEs

Abstract: I will discuss joint work with Lenya Ryzhik on a voting model on a branching Brownian motion that speeds up by a constant factor \(\gamma\) every time it branches. We analyze this model via a connection to a nonlocal reaction-diffusion equation. We show that, under certain assumptions on the voting model, there is a phase transition in \(\gamma\), below which the position of the initial particle asymptotically has a nontrivial effect on the overall vote, and above which it does not.

Host: Le Chen