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. 

As of September 2019, I am the primary investigator for NSF DMS Grant 1855516: Multitype Particle Systems.
As of April 2020, I am the primary investigator on the NSF RAPID Grant 2028892: Quarantined Networks and the Spread of COVID-19

See my CV and 


PAPERS reverse arXiv postdate; *undergraduate

30. Three-velocity coalescing ballistic annihilation
Luis Benitez*, Maximus Redman*, Lily Reeves

29. Modeling COVID-19 spread in small colleges
arXiv (In revision at PLOS One)
Riti Bahl*, Nicole Eikmeier, Alexandra Fraser*, Felicia Keesing, Kukai Nakahata*, Lily Z. Wang

28. Particle density in diffusion-limited annihilating systems
Tobias Johnson, Hanbaek Lyu, David Sivakoff

27. Parking on supercritical Galton-Watson trees
Riti Bahl*,  Philip Barnet*
26. Chase-escape with death on trees
arXiv (To appear in the Annals of Probability)
Erin Beckman, Keisha Cook, Nicole Eikmeier, Sarai Hernandez-Torres
25. Two-type annihilating systems on the complete and star graph
arXiv (In revision at Stochastic Processes and the Applications)
Irina Cristali*, Yufeng Jiang*, Remy Kassem*, David Sivakoff, Grayson York*

24. Critical percolation and A+B-->2A dynamics
23. SIR epidemics on evolving graphs
arXiv 
Yufeng Jiang*, Remy Kassem*, Grayson York*, Rick Durrett

22. The phase structure of asymmetric ballistic annihilation
Hanbaek Lyu

21. The contact process on periodic trees
arXiv 
Yufeng Jiang*, Remy Kassem*, Grayson York*, Brandon Zhao*,  Xiangying Huang, Rick Durrett
20. Cover time for the frog model on trees
Forum of Math, Sigma 
Christopher Hoffman, Tobias Johnson

19. The frog model on trees with drift
Electronic Communications in Probability 
Erin Beckman, Natalie Frank*, Yufeng Jiang*, Si Tang
18. Coexistence in chase escape
Rick Durrett, Si Tang
17. The upper threshold in ballistic annihilation
Debbie Burdinski*, Shrey Gupta*

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

15. Poisson percolation on the square lattice
Irina Cristali*, Rick Durrett

14. Parking on transitive unimodular graphs
Annals of Applied Probability 
Janko Gravner, Hanbaeck Lyu, David Sivakoff

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

12. Asymptotic shape of the Brownian frog model
Erin Beckman, Emily Dinan, Rick Durrett, Ran Huo

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

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

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

8. Ewens sampling and invariable generation
Combinatorics, Probability, and Computing  
Gerandy Brito, Christopher Fowler, Avi Levy

7. Stochastic orders and the frog model
Tobias Johnson

6. The critical density for the frog model is the degree of the tree
Tobias Johnson

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

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

3. From transience to recurrence with Poisson tree frogs
Christopher Hoffman, Tobias Johnson

2. Choices, intervals and equidistribution
1. Recurrence and transience for the frog model on trees
Christopher Hoffman, Tobias Johnson
















A schematic of the network in our spatial model for COVID-19 spread through a small college.


An epidemic on an evolving network (from Grayson York).



Oriented Poisson percolation and the critical threshold (from Irina Cristali).

Chase-escape (from Si Tang).


Diffusion limited annihilation (from Hanbaek Lyu).



Asymmetric ballistic annihilation (from Hanbaek Lyu).

Parking on a random tree (from Curien and Hénard).


The Brownian frog model (from Erin Beckman).

A path in a weighted Catalan number.



The rainstick process.