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
[Annals of Probability (to appear)] [arXiv] [Presentation at msft res]
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.

Interval fragmentation

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

Coalescing random walk

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


The bullet problem

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

Random permutations

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


9. 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


10. Cover time for the frog model on the complete graph
[to appear in Rose-Hulman Journal of Undergraduate Research][arXiv] 
Nikki Carter*, Brittany Dygert*, Stephen Lacina*, Collin Litterell
*, Austin Stromme*. UW REU Aug 2015.

11. 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.


Kakutani fragmentation in two dimensions.


The max-2 process.



A renewal property in the bullet process.



The number of ESF(x,n) permutations needed to invariably generate S_n.


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


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