Published (8)

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

Stochastic orders and the frog model
Tobias Johnson, and Matthew Junge. 2018.

Recurrence and transience for the frog model on trees
Christopher Hoffman, Tobias Johnson, and Matthew Junge. 2017.

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

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

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

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

Choices, intervals and equidistribution
Matthew Junge. 2015.


In revision (3)

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

The upper threshold in ballistic annihilation
Journal of Statistical Physics [arxiv
Debbie Burdinski*, Shrey Gupta*, Matthew Junge. 2018.

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

Submitted (8)

The frog model on trees with drift
Erin Beckman, Natalie Frank*, Yufeng Jiang*, Matthew Junge, Si Tang. 2018.

Coexistence in chase escape
arXiv
Rick Durrett, Matthew Junge, Si Tang. July, 2018.

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

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

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

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

Block size in Geometric(p)-biased permuataoins
Irina Cristali*, Vinit Ranjan*, Jake Steinberg*, Erin Beckman, Rick Durrett, Matthew Junge, James Nolen. 2017.

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



Undergrad Research Supervised


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

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.