Jonathan Hermon

I am a Ph.D. student in the Department of Statistics, University of California, Berkeley, advised by Allan Sly. Before coming to Berkeley I received my M.Sc degree in Mathematics from the Weizmann institute of science with Itai Benjamini serving as my advisor.

My graduate research has been mostly concentrated on problems in discrete probability theory with a special emphasis on problems related to the theory of mixing times of Markov chains and the cutoff phenomenon. Besides that, I have also worked on particle systems driven by random walks and on dependent percolation. I am especially interested in the interaction between geometric properties of graphs, random walk and percolation.




Education


  • University of California, Berkeley: Ph.D. Student, Department of Statistics, Fall 2012-Present.
  • Weizmann Institute of Science: M.Sc., Mathematics. Faculty of Mathematics and Computer Science, Fall 2010-2012.
  • Employment


  • Microsoft Research, Redmond: Research Intern (twice), May 26-Aug 22, 2014 and June 29-Sep 18, 2015. Mentored by Yuval Peres.
  • Research


    Publications and preprints [arXiv]

    • 1. Characterization of the cutoff phenomenon for reversible Markov chains With Yuval Peres and Riddhipratim Basu.
      To appear in Annals of Probability. Extended abstract appeared in SODA 2015. arXiv.
    • 2. The power of averaging at two consecutive time steps: Proof of a mixing conjecture by Aldous and Fill With Yuval Peres.
      To appear in Annales de l’Institut Henri Poincaré, 2016. arXiv.
    • 3. Total variation and separation cutoffs are not equivalent and neither one implies the other With Hubert Lacoin and Yuval Peres.
      Electronic Journal of Probability, 2016. arXiv.
    • 4. On sensitivity of uniform mixing times.
      To appear in Annales de l’Institut Henri Poincaré, 2016. arXiv.
    • 5. On giant components and treewidth in the layers model With Uri Feige and Daniel Reichman.
      Random Structures and Algorithms, 2016. arXiv.
    • 6. Rapid mixing of hypergraph independent set With Allan Sly and Yumeng Zhang.
      2016. Preprint at arXiv.
    • 7. A characterization of L2 mixing and hypercontractivity via hitting times and maximal inequalities With Yuval Peres.
      Submitted. 2016. Preprint at arXiv.
    • 8. On sensitivity of mixing times and cutoff With Yuval Peres.
      Preprint at arXiv.
    • 9. Rapid Social connectivity With Itai Benjamini.
      2016. Preprint at arXiv.
    • 10. The social network model on infinite graphs With Ben Morris, Chuan Qin and Allan Sly.
      Submitted. 2016. Preprint at arXiv.
    • 11. Frogs on trees?
      Submitted. 2016. Preprint at arXiv.
    • 12. On an epidemic model on finite graphs With I. Benjamini, L.R. Fontes and F.P. Machado.
      2016. Preprint at arXiv.
    • 13. Infinite and giant components in the layers percolation model.
      Submitted. 2016. Preprint at arXiv.
    • 14. A technical report on hitting times, mixing and cutoff.
      Preprint at arXiv.

    In Preparation

    • Which connected spatial networks on random points satisfy a shape theorem With David Aldous.

    Teaching


    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


    University of California, Berkeley
    Department of Statistics
    385 Evans Hall,
    Berkeley, CA 94720-3860
    Email: jonathan.hermon@berkeley.edu