Tobias Johnson

I'm an associate professor in mathematics at the College of Staten Island, part of the CUNY system. My collaborators include Ioana Dumitriu, Soumik Pal, Chris Hoffman, Hanbaek Lyu, Elliot Paquette, Matt Junge, Larry Goldstein, and Raphaël Lachièze-Rey, Moumanti Podder, David Sivakoff, Fiona Skerman, Leo Rolla, and Erol Peköz.

I study probability and combinatorics. For the 2024–2025 academic year, I'm on sabbatical at Uppsala University in Sweden. For more about my research, see my c.v. and my papers below. You can also find all of my papers on my arXiv page.

Papers

• Cutoff for activated random walk, with Christopher Hoffman, Matthew Junge, and Josh Meisel. arXiv
  Preprint.
• The hockey-stick conjecture for activated random walk, with Christopher Hoffman and Matthew Junge. arXiv
  Submitted.
• The density conjecture for activated random walk, with Christopher Hoffman and Matthew Junge. arXiv
  Submitted.
• 2023
  Particle density in diffusion-limited annihilating systems, with Matthew Junge, Hanbaek Lyu, and David Sivakoff. arXiv
  Ann. Probab., 51(6):2301–2344, 2023.
• 2022
  Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes, with Erol Peköz. arXiv
  Stochastic Process. Appl., 152 (2022), 1–31.
• Diffusion-limited annihilating systems and the increasing convex order, with Riti Bahl, Philip Barnet, and Matthew Junge. arXiv
  Electron. J. Probab., 27, no. 84 1–19, 2022.
• Continuous phase transitions on Galton–Watson trees. arXiv
  Combin. Probab. Comput., 31(2):184–367, 2022.
• 2020
  Random tree recursions: which fixed points correspond to tangible sets of trees?, with Moumanti Podder, and Fiona Skerman. arXiv
  Random Structures Algorithms, 56(3):796–837, 2020.
• 2019
  Cover time for the frog model on trees, with Christopher Hoffman and Matthew Junge. arXiv
  Forum Math. Sigma, 7, e41 1–49, 2019.
• Infection spread for the frog model on trees, with Christopher Hoffman and Matthew Junge. arXiv
  Electron. J. Probab., 24, no. 112 1–29, 2019.
• Sensitivity of the frog model to initial conditions, with Leonardo T. Rolla. arXiv
  Electron. Commun. Probab., 24, no. 29 1-9, 2019.
• 2018
  Stochastic orders and the frog model, with Matthew Junge. arXiv
  Ann. Inst. H. Poincaré Probab. Statist., 54(2):1013–1030, 2018.
• Bounds to the normal for proximity region graphs, with Larry Goldstein and Raphaël Lachièze-Rey. arXiv
  Stochastic Process. Appl., 128(4):1208–1237, 2018.
• Size biased couplings and the spectral gap for random regular graphs, with Nicholas Cook and Larry Goldstein. arXiv
  Ann. Probab., 46(1):72–125, 2018.
• 2017
  Recurrence and transience for the frog model on trees, with Christopher Hoffman and Matthew Junge. arXiv
  Ann. Probab., 45(5):2826–2854, 2017.
• Local limit of the fixed point forest, with Anne Schilling and Erik Slivken. arXiv
  Electron. J. Probab., 22 (2017), no. 18, 1–26.
• 2016
  The critical density for the frog model is the degree of the tree, with Matthew Junge. arXiv
  Electron. Commun. Probab., 21 (2016), no. 82, 1–12.
• From transience to recurrence with Poisson tree frogs, with Christopher Hoffman and Matthew Junge. arXiv
  Ann. Appl. Probab., 26(3):1260–1635, 2016.
• The Marčenko-Pastur law for sparse random bipartite biregular graphs, with Ioana Dumitriu. arXiv
  Random Structures Algorithms, 48(2):313–340, 2016.
• 2015
  Exchangeable pairs, switchings, and random regular graphs. arXiv
  Electron. J. Combin., 22(1):P1.33, 2015.
• Quantitative small subgraph conditioning, with Elliot Paquette. arXiv
  Perpetual preprint.
• 2014
  Cycles and eigenvalues of sequentially growing random regular graphs, with Soumik Pal. arXiv
  Ann. Probab., 42(4):1396–1437, 2014.
• Eigenvalue fluctuations for random regular graphs. arXiv
  Ph.D. thesis, University of Washington, 2014.
• 2013
  Functional limit theorems for random regular graphs, with Ioana Dumitriu, Soumik Pal, and Elliot Paquette. arXiv
  Probab. Theory Related Fields, 156(3–4):921–975, 2013.
• 2009
  On universal cycles for multisets, with Glenn Hurlbert and Joshua Zahl. arXiv
  Discrete Math., 309::5321–5327, 2009.
• 2007
  Cache-Oblivious Traversals of an Array's Pairs. pdf
  Undergraduate senior project.