Jonathan Hermon

I am an assistant professor at the mathematics department at the University of British Columbia. From 2017 until 2020 I was a research associate in the Statistical Laboratory, part of the DPMMS at the University of Cambridge.

Research interests

• 1. Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution.
  With Tom Hutchcroft. (2020). To appear in Inventiones Mathematicae Preprint at arXiv.
• 2. Characterization of the cutoff phenomenon for reversible Markov chains.
  With Yuval Peres and Riddhipratim Basu. Annals of Probability, 45.3 (2017), 1448-1487. Extended abstract appeared in SODA 2015. arXiv.
• 3. Universality of cutoff for graphs with an added random matching.
  With Allan Sly and Perla Sousi. (2021). To appear in Annals of Probability. Preprint at arXiv.
• 4. A characterization of L2 mixing and hypercontractivity via hitting times and maximal inequalities.
  With Yuval Peres. Probability Theory and Related Fields 170 (2018), 769-800. arXiv.
• 5. No percolation at criticality on certain groups of intermediate growth.
  With Tom Hutchcroft. (2018). To appear in International Mathematics Research Notices Preprint at arXiv.
• 6. A comparison principle for random walk on dynamical percolation.
  With Perla Sousi. To appear in Annals of Probab. (2019). Preprint at arXiv.
• 7. The exclusion process mixes (almost) faster than independent particles.
  With Richard Pymar. To appear in Annals of Probab. (2019) Preprint at arXiv.
• 8. On sensitivity of uniform mixing times.
  Annales de l’Institut Henri Poincaré 54.1 (2018), 234-248.

Full list of publications [arXiv]

• 1. Universality of cutoff for graphs with an added random matching.
  With Allan Sly and Perla Sousi. (2021). To appear in Annals of Probability. Preprint at arXiv.
• 2. Entropy dissipation estimates for inhomogeneous zero-range processes.
  With Justin Salez. To appear in Annals of Applied Probab. (2020). Preprint at arXiv.
• 3. Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution.
  With Tom Hutchcroft. (2020). To appear in Inventiones Mathematicae Preprint at arXiv.
• 4. The exclusion process mixes (almost) faster than independent particles.
  With Richard Pymar. To appear in Annals of Probab. (2019) Preprint at arXiv.
• 5. The interchange process on high-dimensional products.
  With Justin Salez. To appear in Annals of Applied Probab. (2019). Preprint at arXiv.
• 6. A comparison principle for random walk on dynamical percolation.
  With Perla Sousi. To appear in Annals of Probab. (2019). Preprint at arXiv.
• 7. No percolation at criticality on certain groups of intermediate growth.
  With Tom Hutchcroft. (2018). To appear in International Mathematics Research Notices Preprint at arXiv.
• 8. The social network model on infinite graphs.
  With Ben Morris, Chuan Qin and Allan Sly. To appear in Annals of Applied Probability. Preprint at arXiv.
• 9. On an epidemic model on finite graphs
  With I. Benjamini, L.R. Fontes and F.P. Machado. To appear in Annals of Applied Probability. Preprint at arXiv.
• 10. Cutoff for the mean-field zero-range process with bounded monotone rates.
  With Justin Salez. (2018). To appear in Annals of Probability. Preprint at arXiv.
• 11. Rapid Social connectivity.
  With Itai Benjamini. Electronic Journal of Probability, 24.32 (2019). arXiv.
• 12. Recurrence of Markov chain traces.
  With Itai Benjamini. To appear in Annales de l’Institut Henri Poincaré. Preprint at arXiv.
• 13. A version of Aldous' spectral-gap conjecture for the zero range process.
  With Justin Salez. To appear in Annals of Applied Probability. Preprint at arXiv.
• 14. Cutoff for Ramanujan graphs via degree inflation.
  Electron. Commun. Probab. 22.45 (2017). arXiv.
• 15. Reversibility of the non-backtracking walk.
  To appear in Annales de l’Institut Henri Poincaré. Preprint at arXiv.
• 16. Characterization of the cutoff phenomenon for reversible Markov chains.
  With Yuval Peres and Riddhipratim Basu. Annals of Probability, 45.3 (2017), 1448-1487. Extended abstract appeared in SODA 2015. arXiv.
• 17. A characterization of L2 mixing and hypercontractivity via hitting times and maximal inequalities.
  With Yuval Peres. Probability Theory and Related Fields 170 (2018), 769-800. arXiv.
• 18. The power of averaging at two consecutive time steps: Proof of a mixing conjecture by Aldous and Fill.
  With Yuval Peres. Annales de l’Institut Henri Poincaré 53.4 (2017), 2030-2042. arXiv.
• 19. Total variation and separation cutoffs are not equivalent and neither one implies the other.
  With Hubert Lacoin and Yuval Peres. Electronic Journal of Probability, 21.44 (2016). arXiv.
• 20. On sensitivity of uniform mixing times.
  Annales de l’Institut Henri Poincaré 54.1 (2018), 234-248. arXiv.
• 21. A spectral characterization for concentration of the cover time.
  To appear in Journal of Theoretical Probability Preprint at arXiv.
• 22. On giant components and treewidth in the layers model.
  With Uri Feige and Daniel Reichman. Random Structures and Algorithms 48.3 (2016), 524-545. arXiv.
• 23. Rapid mixing of hypergraph independent set.
  with Allan Sly and Yumeng Zhang. Random Structures and Algorithms, 54.4 (2019). arXiv.
• 24. On sensitivity of mixing times and cutoff.
  With Yuval Peres. Electron. J. Probab. 23.26 (2018). arXiv.
• 25. Frogs on trees?
  Electron. J. Probab. 23.17 (2018). arXiv.
• 26. A technical report on hitting times, mixing and cutoff.
  ALEA 15 (2018), 101-120. arXiv.
• 27. Infinite and Giant Components in the Layers Percolation Model.
  ALEA 15 (2018), 121-149. arXiv.

Preprints

• 28. Sensitivity of mixing times of Cayley graphs.
  With Gady Kozma. (2020). Preprint at arXiv.
• 29. Modified log-Sobolev inequalities for strong-Rayleigh measures.
  With Justin Salez. (2019). Preprint at arXiv.
• 30. Some inequalities for reversible Markov chains and branching random walks via spectral optimization.
  Preprint at arXiv.
• 31. Cutoff for Random Walks on Upper Triangular Matrices.
  With Sam Olesker-Taylor (2021). Preprint at arXiv.
• 32. Cutoff for Almost All Random Walks on Abelian Groups.
  With Sam Olesker-Taylor. (2021). Preprint at arXiv.
• 33. Geometry of Random Cayley Graphs of Abelian Groups.
  With Sam Olesker-Taylor. (2021). Preprint at arXiv.
• 34. Covering a graph with independent walks.
  With Perla Sousi. (2021). Preprint at arXiv.
• 35. Mean Field Behavior during the Big Bang for Coalescing Random Walk.
  With Shuangping Li, Dong Yao and Lingfu Zhang. (2021). Preprint at arXiv.
• 36. A direct comparison between the mixing time of the interchange process with "few" particles and independent random walks.
  With Richard Pymar. (2021). Preprint at arXiv.

• 1. Random Cayley graphs, Stanford Probability seminar, May 2020.
  . Slides.