Jonathan Hermon 
I am a research associate in the Statistical Laboratory, part of the DPMMS at the University of Cambridge.
I received my PhD from UC Berkeley, where I was mentored by Allan Sly.
Before coming to Cambridge I was a postdoc at the Faculty of Mathematics at the Weizmann institute of science.
I was an intern in the Microsoft Research Theory Group in the summers of 2014 and 2015, under the mentorship of Yuval Peres.


My research is in discrete probability theory with a special emphasis on problems related to the theory of mixing times of Markov chains and the cutoff phenomenon. I am also working on particle systems and percolation. Research Statement, C.V.

Papers
 1. 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.
 2. Cutoff for the meanfield zerorange process with bounded monotone rates.
With Justin Salez. (2018). To appear in Annals of Probability. Preprint at arXiv.
 3. Rapid Social connectivity.
With Itai Benjamini. Electronic Journal of Probability, 24.32 (2019). arXiv.
 4. Recurrence of Markov chain traces.
With Itai Benjamini. To appear in Annales de l’Institut Henri Poincaré. Preprint at arXiv.
 5. A version of Aldous' spectralgap conjecture for the zero range process.
With Justin Salez. To appear in Annals of Applied Probability. Preprint at arXiv.
 6. Cutoff for Ramanujan graphs via degree inflation.
Electron. Commun. Probab. 22.45 (2017). arXiv.
 7. Reversibility of the nonbacktracking walk.
To appear in Annales de l’Institut Henri Poincaré. Preprint at arXiv.
 8. Characterization of the cutoff phenomenon for reversible Markov chains.
With Yuval Peres and Riddhipratim Basu.
Annals of Probability, 45.3 (2017), 14481487. Extended abstract appeared in SODA 2015. arXiv.
 9. A characterization of L2 mixing and hypercontractivity via hitting times and maximal inequalities.
With Yuval Peres. Probability Theory and Related Fields 170 (2018), 769800. arXiv.
 10. 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), 20302042. arXiv.
 11. 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.
 12. On sensitivity of uniform mixing times.
Annales de l’Institut Henri Poincaré 54.1 (2018), 234248.
arXiv.
 13. On giant components and treewidth in the layers model.
With Uri Feige and Daniel Reichman. Random Structures and Algorithms 48.3 (2016), 524545. arXiv.
 14. Rapid mixing of hypergraph independent set.
with Allan Sly and Yumeng Zhang. Random Structures and Algorithms, 54.4 (2019). arXiv.
 15. On sensitivity of mixing times and cutoff.
With Yuval Peres. Electron. J. Probab. 23.26 (2018). arXiv.
 16. Frogs on trees?
Electron. J. Probab. 23.17 (2018). arXiv.
 17. A technical report on hitting times, mixing and cutoff.
ALEA 15 (2018), 101120. arXiv.
 18. Infinite and Giant Components in the Layers Percolation Model.
ALEA 15 (2018), 121149. arXiv.
Preprints
 19. The interchange process on highdimensional products.
With Justin Salez. (2019). Preprint at arXiv.
 20. Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution.
With Tom Hutchcroft. (2019). Preprint at arXiv.
 21. Entropy dissipation estimates for inhomogeneous zerorange processes.
With Justin Salez. (2019). Preprint at arXiv.
 22. A comparison principle for random walk on dynamical percolation.
With Perla Sousi. (2019). Preprint at arXiv.
 23. Modified logSobolev inequalities for strongRayleigh measures.
With Justin Salez. (2019). Preprint at arXiv.
 24. Cutoff for Mixing Times on Random Abelian Cayley Graphs.
With Sam Thomas. (2018). Preprint at arXiv.
 25. No percolation at criticality on certain groups of intermediate growth.
With Tom Hutchcroft. (2018). Preprint at arXiv.
 26. The exclusion process mixes (almost) faster than independent particles.
With Richard Pymar. Preprint at arXiv.
 27. A spectral characterization for concentration of the cover time.
Preprint at arXiv.
 28. The social network model on infinite graphs.
With Ben Morris, Chuan Qin and Allan Sly. Preprint at arXiv.
In preparation (draft available upon request)
LogSobolev inequalities for generalized exclusion processes revisited. With Justin Salez.
Transitive graphs with proportional mixing and hitting times scale to the unitcircle. With Itai Benjamini, Romain Tessera and Matthew Tointon.

Teaching
Lent 2019: Mixing times of Markov chains (Part III)
I have served as a GSI (Graduate Student Instructor) for the following courses at Berkeley.
Fall 2016: Stat 150, Stochastic Processes.
Spring 2015: Stat 150, Stochastic Processes.
Spring 2014: Stat 150, Stochastic Processes.
Spring 2013: Stat 134, Introduction to Probability.
Spring 2012: Stat 134, Introduction to Probability.

Contact
Centre for Mathematical Sciences
Wilberforce Road
Cambridge
CB3 0WB
Office: D2.01
Email: jh2129(at)statslab.cam.ac.uk
