# 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 on kinetically constrained spin models and the closely related bootstrap percolation, as well as on dimer model dynamics.

## 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

Preprints: 3, 1; papers: 16, 12, 2.

### Preprints

1. Kinetically constrained models out of equilibrium
with F. Toninelli
Submitted pdf, arXiv
2. The maximal running time of hypergraph bootstrap percolation
with L. Lichev
Submitted pdf, arXiv
3. Refined universality for critical KCM: upper bounds
Submitted pdf, arXiv, slides

### Papers (published or to appear)

1. Fredrickson-Andersen model in two dimensions
with F. Martinelli and C. Toninelli
ESAIM: Proceedings and Surveys (to appear) pdf, arXiv
2. The normal contraction property for non-bilinear Dirichlet forms
with G. Brigati
Potential analysis (to appear) pdf, arXiv, journal
3. 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
4. Subcritical bootstrap percolation via Toom contours
with R. Szabó
Electronic communications in Probability 27 (2022). 13+2pp. pdf including the online appendix, arXiv, journal
5. Bootstrap percolation, probabilistic cellular automata and sharpness
Journal of Statistical Physics, 187 (2022), no. 3, Article 21. 17pp. pdf, arXiv, journal
6. Generalised oriented site percolation
with R. Szabó
Markov Processes and Related Fields, 28 (2022), no. 2. 28pp. pdf, arXiv, journal
7. 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
8. 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
9. 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
10. Bisection for kinetically constrained models revisited
Electronic Communications in Probability 26 (2021). 10pp. pdf, arXiv, journal, slides
11. 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
12. $$\mathcal{U}$$-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
13. 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
14. 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
15. Strong Ramsey games in unbounded time
with S. David and M. Tiba
European Journal of Combinatorics, 86 (2020), 103096. 26pp. pdf, arXiv, journal
16. 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
17. 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
18. 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

### 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
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.

## Collaborators

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

Initialised: 04.2017
Last update: 03.2023