5 papers
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 Rodríguez
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…
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 approaches the sleep probability as and provide the first-order correction.
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 with uniform or central driving exhibits cutoff at times the critical den…