57 citations · 257 across the 30 of their papers we have counts for
4 papers · 2 filters
Ewens sampling and invariable generation
Gerandy Brito, Christopher Fowler, Matthew Junge +1
We study the number of random permutations needed to invariably generate the symmetric group, , when the distribution of cycle counts has the strong -logarithmic property.…
The bullet problem with discrete speeds
Brittany Dygert, Christoph Kinzel, Jennifer Zhu +3
Bullets are fired, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that the second fastest bullet s…
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…
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…