Matthew Junge

Education

Ph.D., Mathematics, University of Washington Seattle WA

M.S., Mathematics, University of Washington Seattle WA

B.A., Philosophy, University of Washington Seattle WA

B.S., Mathematics, University of Washington Seattle WA

Journal Articles

(2025). Cutoff for activated random walk.

(2025). Mean-field limit for activated random walk on the integer lattice.

(2025). Chase-escape with conversion as a multiple sclerosis lesion model.

(2025). Diffusion-limited annihilating-coalescing systems. Electronic Journal of Probability, 30.

(2025). The frog model with death revisited.

(2024). Arrivals are universal in coalescing ballistic annihilation. ALEA, 21.

Bailey, E., Junge, M., & Liu, J. (2024). Critical drift estimates for the frog model on trees. Electronic Journal of Probability, 29.

Junge, M. (2024). Reflections on Teaching Mathematics in Prisons . Journal of Humanistic Mathematics, 14(1). 266--270.

Mathews Jr, P. (2024). Improved critical drift estimates for the frog model on trees. Electronic Communications in Probability, 29.

(2024). Distance-dependent chase-escape on trees. New Zealand Journal of Mathematics, 55.

(2024). The density conjecture for activated random walk.

(2023). A stochastic combustion model with thresholds on trees. Journal of Statistical Physics, 190.

(2023). Non-universality in clustered ballistic annihilation. Electronic Communications in Probability, 28. 1-12.

Benitez, L., Junge, M., Lyu, H., Redman, M., & Reeves, L. (2023). Three-velocity coalescing ballistic annihilation. Electronic Journal of Probability, 28. 1-18. In Progress.

(2023). Four-parameter coalescing ballistic annihilation. Journal of Statistical Physics, 191.

Johnson, T., Junge, M., Lyu, H., & Sivakoff, D. (2023). Particle density in diffusion-limited annihilating systems. Annals of Probability, 51(6). 2301--2344.

Bahl, R., Barnet, P., Johnson, T., & Junge, M. (2022). Diffusion-limited annihilating systems and the increasing convex order. Electronic Journal of Probability, 27. 1-19.

Junge, M., Li, S., Samaranayake, S., & Zalesak, M. (2022). Safe reopening of university campuses is possible with COVID-19 vaccination. PLOS One, 17(7).

(2022). Chase-escape on the configuration model. Electronic Communications in Probabality, 27: 1-14 (2022). DOI. 1-14.

Junge, M., & Lyu, H. (2022). The phase structure of asymmetric ballistic annihilation. Annals of Applied Probability, 32(5). 3797-3816.

Beckman, E., Cook, K., Eikmeier, N., Hernandez-Torres, S., & Junge, M. (2021). Chase-escape with death on trees. The Annals of Probability, 49(5). 2540-2547.

Cristali, I., Jiang, Y., Junge, M., Kassem, R., Sivakoff, D., & York, G. (2021). Two-type annihilating systems on complete and star graphs. Stochastic Processes and their Applications, 139. 321-342.

Bahl, R., Eikmeier, N., Fraser, A., Junge, M., Keesing, F., Nakahata, K., & Wang, L. Z. (2020). Modeling COVID-19 spread in small colleges. PLOS One, PLOS One 16(8)(e0255654). 24.

Junge, M. (2020). Critical Percolation and A+ B¿ 2A Dynamics. Journal of Statistical Physics, 181(2). 738--751.

Durrett, R., Junge, M., & Tang, S. (2020). Coexistence in chase-escape. Electronic Communications in Probability, 25. 1--14.

Cristali, I., Junge, M., & Durrett, R. (2019). Poisson percolation on the square lattice. Latin American Journal of Probability and Statistics (ALEA), 16. 429-437.

Burdinski, D., Gupta, S., & Junge, M. (2019). The upper threshold in ballistic annihilation. Latin American Journal of Probability and Statistics (ALEA), 16. 1077-1087.

Damron, M., Gravner, J., Junge, M., Lyu, H., & Sivakoff, D. (2019). Parking on transitive unimodular graphs. The Annals of Applied Probability, 29(4). 2089--2113.

Cristali, I., Junge, M., & Durrett, R. (2019). Poisson percolation on the oriented square lattice. Stochastic Processes and their Applications, 130(2). 488--502.

Hoffman, C., Johnson, T., & Junge, M. (2019). Cover time for the frog model on trees. Forum of Mathematics, Sigma, 7(41). 49.

Hoffman, C., Johnson, T., & Junge, M. (2019). Infection spread for the frog model on trees. Electronic Journal of Probability, 24. 1--29.

Bahl, R., Barnet, P., & Junge, M. (2019). Parking on supercritical Galton-Watson trees. Latin American Journal of Probability and Statistics (ALEA), (18). 1801-1815.

Dygert, B., Kinzel, C., Junge, M., Raymond, A., Slivken, E., & Zhu, J. (2019). The bullet problem with discrete speeds. Electronic Communications in Probability, 24. 1--11.

Beckman, E., Frank, N., Jiang, Y., Junge, M., & Tang, S. (2019). The frog model on trees with drift. Electronic Communications in Probability, 24. 1--10.

Brito, G., Fowler, C., Junge, M., & Levy, A. (2018). Ewens sampling and invariable generation. Combinatorics, Probability and Computing, 27(6). 853--891.

Beckman, E., Dinan, E., Durrett, R., Huo, R., & Junge, M. (2018). Asymptotic behavior of the Brownian frog model. Electronic Journal of Probability, 23. 1--19.

Foxall, E., Hutchcroft, T., & Junge, M. (2018). Coalescing random walk on unimodular graphs. Electronic Communications in Probability, 23. 1--10.

Johnson, T., & Junge, M. (2018). Stochastic orders and the frog model. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 54(2). 1013--1030.

Cristali, I., Ranjan, V., Steinberg, J., Beckman, E., Durrett, R., Junge, M., & Nolen, J. (2018). Block size in Geometric p-biased permutations. Electronic Communications in Probability, 23. 1--10.

Hoffman, C., Johnson, T., & Junge, M. (2017). Recurrence and transience for the frog model on trees. The Annals of Probability, 45(5). 2826--2854.

Hoffman, C., Johnson, T., & Junge, M. (2016). From transience to recurrence with Poisson tree frogs. The Annals of Applied Probability, 26(3). 1620--1635.

Benjamini, I., Foxall, E., Gurel-Gurevich, O., Junge, M., & Kesten, H. (2016). Site recurrence for coalescing random walk. Electronic Communications in Probability, 21. 1--12.

Junge, M. (2015). Choices, intervals and equidistribution. Electronic Journal of Probability, 20. 1--18.

The hockey-stick conjecture for activated random walk.

Media Contributions

(2020). WAMC Public Radio.

(2020). WAMC Public Radio.

Presentations

Junge, M. The Density Conjecture for Activated Random Walk. Percolation Today.

Junge, M. The Density Conjecture for Activated Random Walk. NYU Probability Seminar. New York University

Junge, M. How REU?. Fordham University

Junge, M. Why is nature critical?. Ideas Seaminar: University of North Carolina.

Junge, M. Simple Probability Questions. ourfam.

Junge, M. (2025, January 24). The frog model on trees. Los Angeles Probability Forum. CalTech

Junge, M. The Density Conjecture for Activated Random Walk. Cornell Probability Seminar.

Junge, M. Prison Education. Museum of Math QED. Online: Museum of Math.

Junge, M. The frog model on trees. CUNY Probability Seminar.

Junge, M. The frog model on trees. University of Madison Probability Seminar.

Junge, M. Chase-escape. Mathematical Biology Seminar. New Jersey Institute of Technology: New Jersey Institute of Technology.

Junge, M. Ballistic Annihilation. Duke Probability Seminar.

Junge, M. Ballistic Annihilation. Georgia Tech Stochastics Seminar.

Junge, M. Ballistic Annihilation. University of Pennsylvania and Temple University Probability Seminar.

Junge, M. Ballistic Annihilation. CUNY Probability Seminar.

Junge, M. Ballistic Annihilation. Cornell University Probability Seminar.

Junge, M. Ballistic Annihiliation. Markov Chains with Kinetic Constraints and Applications. Banff, Canada: Banff International Research Station.

Junge, M. (2021, September 14). Pandemic REUs. CUNY Probability Seminar. Zoom

Junge, M. (2021, April 14). Modeling COVID-19 Spread in Small Colleges. Baruch College Statistics Seminar. Remote: Baruch College.

Junge, M. (2020, September 9). Modeling COVID-19 Spread in Small Colleges. Mount Holyoke College Mathematics and Statistics Colloquium. Remote: Mount Holyoke.

Junge, M. (2020, September 11). Modeling COVID-19 Spread in Small Colleges. Cornell Center for Applied Mathematics Colloquium. Remote: Cornell University.

Junge, M. (2020, September 1). Modeling COVID-19 Spread in Small Colleges. CUNY Probability Seminar. Remote: CUNY.

Junge, M. (2020, April 16). Modeling COVID-19 Spread in Small Colleges. University of Wisconsin Madison Applied Math Seminar. Remote: University of Wisconsin Madison.

Department

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University

Public