Author

Peter Gracar

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Preprint Aug 2026

Motion helps the contact process: survival below the percolation threshold on Poisson Brownian motions

We consider the SIS contact process on a Poisson system of independent Brownian motions in $\mathbb{R}^d$ of intensity $\eta$. Two particles are in contact when their distance is at most $2r$. An infected particle transmits the infection to a susceptible particle in contact with it at rate $\lambda\in(0,\infty]$, and r...

Peter Gracar · 0 citations

Preprint Aug 2026

Rainbow percolation

We consider the weight-dependent random connection model on a Poisson point process of intensity $\lambda$ on $\mathbb{R}\times(0,1)$ in which the vertices $(x,t)$ and $(y,s)$ are joined precisely when $(t\vee s)|x-y|\le\beta$. Points at distance $d$ are joined with probability $\min(1,\beta/d)^2$, the critical decay o...

Peter Gracar, Benjamin Lees · 0 citations