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. 2017.

2. Choices, intervals and equidistribution
2015.

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

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

6. Stochastic orders and the frog model
Tobias Johnson. 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, Avi Levy. 2016.

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

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

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

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

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

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

15. Poisson percolation on the square lattice
To appear in ALEA
Irina Cristali*, Rick Durrett. 2017.

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

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

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

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

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

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

22. The phase structure of asymmetric ballistic annihilation
Hanbaek Lyu.

23. SIR epidemics on evolving graphs
arXiv
Yufeng Jiang*, Remy Kassem*, Grayson York*, Rick Durrett. 2018.




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).