The frog model

1. From transience to recurrence with Poisson tree frogs
Christopher Hoffman, Tobias Johnson, and Matthew Junge. 2016. 

2. Recurrence and transience for the frog model on trees
Christopher Hoffman, Tobias Johnson, and Matthew Junge. 2014.

3. Stochastic orders and the frog model
[Annales de l'Institut Henri Poincaré (to appear)] [arXiv 
Tobias Johnson, and Matthew Junge. Nov, 2015.

4. The critical density for the frog model is the degree of the tree
Tobias Johnson, and Matthew Junge. Dec, 2016.

5. Infection spread for the frog model on trees
[arXiv 
Christopher Hoffman, Tobias Johnson, and Matthew Junge. 2017.

6. Asymptotic behavior of the Brownian frog model
[arXiv 
Erin Beckman, Emily Dinan, Rick Durrett, Ran Huo, and Matthew    Junge. 2017.

Interval fragmentation

7. Choices, intervals and equidistribution
Matthew Junge. September, 2015.

Annihilating particles

8. Site recurrence for coalescing random walk
Itai Benjamini, Eric Foxall, Ori Gurel-Gurevich, Matthew Junge, Harry Kesten. 2016.

9. The bullet problem with discrete speeds
[arXiv
Brittany Dygert*, Christoph Kinzel*, Jennifer Zhu*, Matthew Junge, Annie Raymond, Erik Slivken. 2016.

9. Parking on transitive unimodular graphs
[arXiv
Janko Gravner, Hanbeck Lyu, Matthew Junge, David Sivakoff. 2017.

Random permutations

10. Ewens sampling and invariable generation
[Combinatorics, Probability, and Computing (to appear)] [arXiv
Gerandy Brito, Christopher Fowler, Matthew Junge, Avi Levy. 2016.


11. Block sizes in two families of regenerative permutations
[arXiv] 
Irina Cristali*, Vinit Ranjan*, Jake Steinberg*, Erin Beckman, Rick Durrett, Matthew Junge, James Nolen. 2016.

Undergraduate Research Supervised


12. Frog model wakeup time on the complete graph
Nikki Carter*, Brittany Dygert*, Stephen Lacina*, Collin Litterell
*, Austin Stromme*.  2016.

13. The Johnny Appleseed random walk. 
[link] 
Carlos Coronado*, Emily Myers*, Austin Tran*. UW REU 2014.

*undergraduate




A figure that led to a proof of recurrence for the frog model on a binary tree.

Cascading frogs down a stair-step fountain to prove a fast cover time.

A coupling in the Brownian frog model.

The max-2 process.



A renewal property in the bullet process.



The rainstick process can be used to generate infinite random permutations.


A 2-dependent arrow model for the Johnny Appleseed random walk.