My research takes a probabilistic approach to particle systems from physics and biology. This includes models for chemical reactions, species proliferation, and epidemic outbreaks. I also study random structures from classical mathematics and computer science such as permutations and fragmented spaces. 

See my CV and 


Published

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

9. Asymptotic behavior of the Brownian frog model
Erin Beckman, Emily Dinan, Rick Durrett, Ran Huo, and Matthew Junge. 2018.

8. Coalescing random walk on unimodular graphs
Eric Foxall, Tom Hutchcroft, Matthew Junge. 2018.

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

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

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

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

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

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

1. Choices, intervals and equidistribution
Matthew Junge. 2015.


In revision

Poisson percolation on the square lattice
Latin American Journal of Probability and Mathematical Statistics [arXiv]
Irina Cristali*, Matthew Junge, Rick Durrett. 2017.

Poisson percolation on the oriented square lattice
Stochastic Processes and their Applications [arXiv]
Irina Cristali*, Matthew Junge, Rick Durrett. 2018.

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.

 
Submitted 

The contact process on periodic trees
arXiv
Yufeng Jiang*, Remy Kassem*, Grayson York*, Brandon Zhao*, Matthew Junge, Xianqying Huang, Rick Durrett. 2018.

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.

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.

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.


*undergraduate

Poisson percolation.

Chase-escape.


Diffusion limited annihilation.

The Brownian frog model.

The max-2 process.




The bullet process.



The Geometric(p) rainstick.



The Johnny Appleseed random walk.