8 papers
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 on an -vertex complete graph with a sink that traps jumping particles with probability . We sho…
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…
The hockey-stick conjecture for activated random walk
Christopher Hoffman, Tobias Johnson, Matthew Junge
We prove a conjecture of Levine and Silvestri that the driven-dissipative activated random walk model on an interval drives itself directly to and then sustains a critical density.…
The frog model with death revisited
Samyah Ahmed, Matthew Junge
We prove that the probability the frog model with death and drift on the -ary tree is recurrent can be made positive and thus is not monotone in the drift parameter.
Chase-escape with conversion on the complete graph
Matthew Junge, Sergio RodrÃguez
We prove that chase-escape with conversion on the complete graph undergoes a phase transition at equal fitness and derive simple asymptotic formulas for the extinction probability,…
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…