Activation

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. 2015.

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

7. Cover time for the frog model on trees
[arXiv 
Christopher Hoffman, Tobias Johnson, and Matthew Junge. 2017.

Percolation

8. Poisson percolation on the square lattice
Irina Cristali*, Matthew Junge, Rick Durrett. December, 2017.

9. Poisson percolation on the oriented square lattice
Irina Cristali*, Matthew Junge, Rick Durrett. June, 2018.

Fragmentation

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

Annihilation

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

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

13. Parking on transitive unimodular graphs
[in revision for Annals of Applied Probability][arXiv
Janko Gravner, Hanbaeck Lyu, Matthew Junge, David Sivakoff. 2017.

14. Coalescing random walk on unimodular graphs
[Electronic Communications in Probability to appear][arxiv
Eric Foxall, Tom Hutchcroft, Matthew Junge. 2018.

15. The upper threshold in ballistic annihilation
[arxiv
Debbie Burdinski*, Shrey Gupta*, Matthew Junge. 2018.

Permutation

16. Ewens sampling and invariable generation
Gerandy Brito, Christopher Fowler, Matthew Junge, Avi Levy. 2016.


17. The asymptotic behavior of the geometric(p) rainstick as p-->0
[arXiv] 
Irina Cristali*, Vinit Ranjan*, Jake Steinberg*, Erin Beckman, Rick Durrett, Matthew Junge, James Nolen. 2016.

Undergrad Research Supervised


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

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

*undergraduate


A coupling in the Brownian frog model.

z
The cluster containing 0 in Poisson percolation.

The parking process at criticality.

The max-2 process.




A renewal property in the bullet process.



The geometric rainstick generates infinite random permutations.



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