Matthew Junge

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20242026

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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…