Harley Kaufman

collaborators

3 papers

math.PR2026

Scaling limit and density conjecture for activated random walk on the complete graph

Matthew Junge, Harley Kaufman, Josh Meisel

We study driven-dissipative activated random walk with sleep probability $p$ on an $n$ -vertex complete graph with a sink that traps jumping particles with probability $q_{n}$ . We sho…

math.PR2025

Asymptotic behavior of the critical density of activated random walk

Harley Kaufman, Josh Meisel

We study the asymptotic behavior of the critical density of the activated random walk model as the sleep rate $I^»$ tends to $0$ and $\infty$ . For large $I^»$ , we prove new lower bou…

math.PR2025

Mean-field limit for activated random walk on the integer lattice

Matthew Junge, Harley Kaufman, Josh Meisel

We show that the critical density for activated random walk on $Z^{d}$ approaches the sleep probability as $d \to \infty$ and provide the first-order correction.