Ivailo Hartarsky's webpage

Research interests

My main research interests lie in probability, especially its interface(s) with combinatorics or (not xor) statistical Physics. More concretely, most of my work is on stochastic dynamics and discrete probability. Namely, I primarily study interacting particle systems and probabilistic cellular automata. Currently, I am working mostly on bootstrap percolation and the closely related kinetically constrained spin models, as well as oriented percolation and related models.

Open access statement

As a general rule, the last (or latest) version of all my papers can be found on arXiv. I generally do not display the published version anywhere, but instead use the final manuscript. I recommend reading the latter over the former, as it has the same content and is often better typeset. For that reason I disregard publisher price when submitting and encourage institutional libraries to invest in good printers instead of journal subscriptions.

Abstracts may differ from venue to venue due to length/citation restrictions. I recommend systematically using the one in the pdf of the latest arXiv version.

My papers can also be found below if I have updated my page recently enough. I only deposit them on HAL once they are published, so please refer to arXiv. I do not deposit full texts on ResearchGate or other platforms to avoid violating publisher copyright.

Publications and preprints

Selected works

Papers: 23, 22, 21, 16, 12, 2.


  1. Local dimer dynamics in higher dimensions
    with L. Lichev and F. Toninelli
    Submitted pdf, arXiv

Papers (published or to appear)

  1. Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
    with H. Duminil-Copin
    Probability Theory and Related Fields (to appear). pdf, arXiv
  2. Kinetically constrained models out of equilibrium
    with F. Toninelli
    Probability and Mathematical Physics (to appear). pdf, arXiv, journal, slides
  3. Refined universality for critical KCM: upper bounds
    Communications in Mathematical Physics 405 (2024). 68+16pp.pdf including the online appendices, arXiv, journal, slides
  4. The maximal running time of hypergraph bootstrap percolation
    with L. Lichev
    SIAM Journal on Discrete Mathematics (to appear) pdf, arXiv
  5. Brownian snails with removal die out in one dimension
    with L. Lichev
    Electronic Communications in Probability 28 (2023). 8pp. pdf, arXiv, journal
  6. Sensitive bootstrap percolation second term
    Electronic Communications in Probability 28 (2023). 7pp. pdf, arXiv, journal
  7. The normal contraction property for non-bilinear Dirichlet forms
    with G. Brigati
    Potential Analysis 60 (2024), 473-488. 16pp. pdf, arXiv, journal
  8. Sharp threshold for the FA-2f kinetically constrained model
    with F. Martinelli and C. Toninelli
    Probability Theory and Related Fields, 185 (2023), no. 3, 993–1037. 45pp. pdf, arXiv, journal, slides
  9. Subcritical bootstrap percolation via Toom contours
    with R. Szabó
    Electronic Communications in Probability 27 (2022). 13+2pp. pdf including the online appendix, arXiv, journal
  10. Bootstrap percolation, probabilistic cellular automata and sharpness
    Journal of Statistical Physics, 187 (2022), no. 3, Article 21. 17pp. pdf, arXiv, journal
  11. Generalised oriented site percolation
    with R. Szabó
    Markov Processes and Related Fields, 28 (2022), no. 2. 28pp. pdf, arXiv, journal
  12. Refined universality for critical KCM: lower bounds
    with L. Marêché
    Combinatorics, Probability & Computing 31 (2022), no. 5, 879-906. 28+16pp. pdf including the online appendix, arXiv, journal, slides
  13. Weakly constrained-degree percolation on the hypercubic lattice
    with B. N. B. de Lima
    Stochastic Processes and their Applications 153 (2022), 128-144. 17pp. pdf, arXiv, journal, slides
  14. Coalescing and branching simple symmetric exclusion process
    with F. Martinelli and C. Toninelli
    The Annals of Applied Probability 32 (2022), no. 4, 2841-2859. 19pp. pdf, arXiv, journal, slides
  15. Bisection for kinetically constrained models revisited
    Electronic Communications in Probability 26 (2021). 10pp. pdf, arXiv, journal, slides
  16. Universality for critical KCM: finite number of stable directions
    with F. Martinelli and C. Toninelli
    The Annals of Probability, 49 (2021), no. 5, 2141-2174. 34 pp. pdf, arXiv, journal, slides
  17. \(\mathcal{U}\)-bootstrap percolation: critical probability, exponential decay and applications
    Annales de l'Institut Henri Poincaré B, Probabilités et Statistiques, 57 (2021), no. 3, 1255-1280. 26pp. pdf, arXiv, journal, slides
  18. Universality for critical KCM: infinite number of stable directions
    with L. Marêché and C. Toninelli
    Probability Theory and Related Fields, 178 (2020), no. 1, 289-326. 38pp. pdf, arXiv, journal, slides
  19. Complexity of two-dimensional bootstrap percolation difficulty: Algorithm and NP-hardness
    with T. R. Mezei
    SIAM Journal on Discrete Mathematics, 34 (2020), no. 2, 1444-1459. 16pp. pdf, arXiv, journal
  20. Strong Ramsey games in unbounded time
    with S. David and M. Tiba
    European Journal of Combinatorics, 86 (2020), 103096. 26pp. pdf, arXiv, journal
  21. Maximum-energy records in glassy energy landscapes
    with M. Baity-Jesi, R. Ravasio, A. Billoire and G. Biroli
    Journal of Statistical Mechanics: Theory and Experiment, 2019, no. 9, 093302. 24pp. pdf, arXiv, journal
  22. The second term for two-neighbour bootstrap percolation in two dimensions
    with R. Morris
    Transactions of the American Mathematical Society, 372 (2019), 6465-6505. 41+14pp. pdf including the online appendix, arXiv, journal, slides
  23. Maximal bootstrap percolation time on the hypercube via generalised snake-in-the-box
    Electronic Journal of Combinatorics, 25 (2018), no. 3, Paper 3.10. 12pp. pdf, arXiv, journal

Surveys and proceedings

  1. Universalité des modèles de percolation bootstrap et cinétiquement contraints en deux dimensions
    Matapli (to appear) pdf, HAL
  2. Fredrickson-Andersen model in two dimensions
    with F. Martinelli and C. Toninelli
    ESAIM: Proceedings and Surveys 74 (2023), 108-118. 11pp. pdf, arXiv, journal

Unpublished supervised written work

  1. Bootstrap percolation and kinetically constrained models: two-dimensional universality and beyond
    supervised by C. Toninelli
    PhD thesis pdf, slides, HAL
    Awarded the Jacques Neveu tesis prize by the SMAI.
    Awarded the solemn tesis prize by the Chancellerie des Universités de Paris.
  2. Percolation bootstrap et modèles cinétiquement contraints
    supervised by C. Toninelli
    ENS Diploma thesis pdf
  3. Glassy dynamics: Trap and Random energy models
    supervised by G. Biroli and J. Salez
    Internship report pdf
  4. Sur l'expérience de Mayer
    supervised by J.-F. Logeais
    TIPE pdf

See my CV for more and feel free to contact me if you are interested.

Talk recordings


Here is a list of my research collaborators and coauthors.
Eleanor Archer, Marco Baity-Jesi, Alain Billoire, Giulio Biroli, Giovanni Brigati, Benoît Dagallier, Stefan David, Damiano de Gaspari, Barbara Dembin, Aurélia Deshayes, Hugo Duminil-Copin, Christophe Garban, Daniel Kious, Brett Kolesnik, Lyuben Lichev, Bernardo de Lima, Laure Marêché, Fabio Martinelli, Otávio Menezes, Tamás Mezei, Rob Morris, Sam Olesker-Taylor, Riccardo Ravasio, Bruno Schapira, Stephen G. Z. Smith, Alexandre Stauffer, Réka Szabó, Vincent Tassion, Augusto Teixeira, Marius Tiba, Cristina Toninelli, Fabio Toninelli, Daniel Valesin, Ahad Zehmakan.
I am a member of the FWF project Random Surfaces: growth, fluctuations and universality of Fabio Toninelli.

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