Andrew Heeszel
The Ohio State University
Title
Limiting speed and fluctuations for the boundary modified contact process
Abstract
In this talk we show a law of large numbers and central limit theorem for the edge speeds of the model (BMCP). The BMCP models an epidemic spreading across the integer lattice $\mathbb{Z}$ with two infection parameters $\lambda_i$ and $\lambda_e$. Starting from a finite infected set, each edge of $\mathbb{Z}$ transmits the infection at rate $\lambda_i$ except for the rightmost and leftmost edges incident to infected vertices, which transmit the infection at rate $\lambda_e$. We study the model when the interior infection rate is at the critical infection rate of the contact process and cannot sustain the infection, while the exterior infection rate $\lambda_e > \lambda_c$. Adding a boost to the exterior infection rates causes the BMCP to no longer be an attractive particle system, requiring new tools in its study. We also show the likelihood of the infection dying out after a long but finite time scales at the stretched exponential rate, in contrast with the supercritical contact process.