Josh Meisel

collaborators

9 papers

math.PR2026

Stationary activated random walk: regularity, heavy tails, and remixing

Tobias Johnson, Matthew Junge, Josh Meisel

We study the stationary state of driven-dissipative activated random walk on an interval of length $n$ and prove that subintervals down to size $lo g n$ have particle density near…

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…

cond-mat.stat-mech2026

Activated random walk exhibits self-organized criticality

Christopher Hoffman, Tobias Johnson, Matthew Junge +1

To explain the ubiquity of power laws and fractals in nature, Bak, Tang, and Wiesenfeld formulated simple conditions for a system to self-organize into a critical state. Dickman, M…

math.PR2026

Explosivity in 1-d Activated Random Walk

Nicolas Forien, Christopher Hoffman, Tobias Johnson +3

We show that Activated Random Walk on $Z$ is explosive above criticality. That is, activating a single particle in a supercritical state of sleeping particles triggers an…

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 $λ$ tends to $0$ and $\infty$ . For large $λ$ , we prove new lower bound…

math.PR2025

Activated random walk on the comb

Matthew Junge, Josh Meisel, Aldo Morelli

The density conjecture for activated random walk on the interval was recently resolved using a new tool called layer percolation. As a step towards understanding how layer percolat…

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.

math.PR2025

Cutoff for activated random walk

Christopher Hoffman, Tobias Johnson, Matthew Junge +1

We prove that the mixing time of driven-dissipative activated random walk on an interval of length $n$ with uniform or central driving exhibits cutoff at $n$ times the critical den…

math.PR2025

The critical velocity of the bullet process appears pathwise

Josh Meisel

In the bullet process, a gun fires bullets in the same direction at independent random speeds, and with independent random time delays between firings. When two bullets collide, th…