47 citations · 297 across the 23 of their papers we have counts for
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math.PR2016★ 15 cited
The critical density for the frog model is the degree of the tree
Tobias Johnson, Matthew Junge
The frog model on the rooted d-ary tree changes from transient to recurrent as the number of frogs per site is increased. We prove that the location of this transition is on the sa…
math.PR2016★ 2 cited
Local limit of the fixed point forest
Tobias Johnson, Anne Schilling, Erik Slivken
Consider the following partial "sorting algorithm" on permutations: take the first entry of the permutation in one-line notation and insert it into the position of its own value. C…
math.PR2016★ 19 cited
Stochastic orders and the frog model
Tobias Johnson, Matthew Junge
The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths…