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 


Publications by arXiv appearance; *undergraduate

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

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

3. From transience to recurrence with Poisson tree frogs
Christopher Hoffman, Tobias Johnson, and Matthew Junge. 2016.
 
4. The critical density for the frog model is the degree of the tree
Tobias Johnson, and Matthew Junge. 2016.

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

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

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

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

9. The bullet problem with discrete speeds
In revision at Electronic Communications in Probability arXiv
Brittany Dygert*, Christoph Kinzel*, Jennifer Zhu*, Matthew Junge, Annie Raymond, Erik Slivken. 2016.

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

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

12. Cover time for the frog model on trees
In revision at Forum of Math, Sigma [arXiv]  
Christopher Hoffman, Tobias Johnson, Matthew Junge. 2017.

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

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

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

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

17. Parking on transitive unimodular graphs
To appear in Annals of Applied Probability
Janko Gravner, Hanbaeck Lyu, Matthew Junge, David Sivakoff. 2017.

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

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

20. The frog model on trees with drift
In revision at Electronic Communications in Probability [arXiv]
Erin Beckman, Natalie Frank*, Yufeng Jiang*, Matthew Junge, Si Tang. 2018.

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

22. The phase structure of asymmetric ballistic annihilation
Matthew Junge, Hanaek Lyu.




Oriented Poisson percolation and the critical threshold.


Unoriented Poisson percolation.

Chase-escape.


Diffusion limited annihilation.

The Brownian frog model.


Ballistic annihilation (from Tournier and Sidoravicius 2017).