Clément Erignoux's web page

Some topics I am currently working on

• Sharpness of the phase transition for a two-dimensional random interlacement percolation model, with A. Teixeira.

• Boundary effects on the non-equilibrium FEP, with H. Da Cunha et M. Simon.

• Mixing time for the FEP on the ring, with B. Massoulié and C. Toninelli.

Submissions and preprints

• Hydrodynamic behavior near dynamical criticality of a facilitated conservative lattice gas , C. Erignoux, A. Roget, A. Shapira and M. Simon, 6p, Submitted to Physical Review E, May 2024,

• Cutoff for the transience and mixing time of a SSEP with traps and consequences on the FEP, C. Erignoux, and B. Massoulié, 39p, Submitted to Communications in Mathematical Physics, May 2024,

• Hydrodynamic limit for a boundary-driven facilitated exclusion process, H. Da Cunha, C. Erignoux, and M. Simon, 45p, Submitted to Annales de l'IHP B - Probabilités et Statistiques, Jan. 2024,

• Stationary Fluctuations For The Facilitated Exclusion Process, C. Erignoux, and L. Zhao, 38p, Submitted to Annales de l'IHP B - Probabilités et Statistiques, Jan. 2023,

Publications

1. [BEL2024] Steady state large deviations for one-dimensional, symmetric exclusion processes in weak contact with reservoirs, A. Bouley, C. Erignoux, and C. Landim, 41p, To appear in Annales de l'IHP B - Probabilités et Statistiques (2024), .

2. [E2024] On the hydrodynamics of active matter models on a lattice, C. Erignoux, 18p, Markov Processes and Related Fields - IRS proceedings, Volume 30, Issue 1, pages 57-80 (2024) - [Bibitex/Bibitem Entries].

3. [ESZ2024] Mapping hydrodynamics for the facilitated exclusion and zero-range processes, C. Erignoux, M. Simon and L. Zhao, 45p, Annals of Applied Probability, Volume 34, Issue 1B (2024) - [Bibitex/Bibitem Entries].

4. [MEJB2023] Exact hydrodynamics and onset of phase separation for an active exclusion process, J. Mason, C. Erignoux, R. Jack and M. Bruna, 31p, Proceedings of the Royal Society A, Volume 479, Number 2279 (2023) - [Bibitex/Bibitem Entries].

5. [ESZ2023] Asymmetric attractive zero-range processes with particle destruction at the origin, C. Erignoux, M. Simon and L. Zhao, 28p, Stochastic Processes and their Applications, Volume 159, pages 1-33 (2023) - [Bibitex/Bibitem Entries].

6. [BES2021] Stefan problem for a non-ergodic facilitated exclusion process, O. Blondel, C. Erignoux, and M. Simon, 49p, Probability and Mathematical Physics, Volume 2, Issue 1, pages 127-178 (2021) - [Bibitex/Bibitem Entries].

7. [E2021] Hydrodynamic limit for an active exclusion process, C.Erignoux, 214p, Mémoires de la SMF, Volume 169 (2021) - [Bibitex/Bibitem Entries].

8. [EGN2020-1] Hydrodynamics for SSEP with non-reversible slow boundary dynamics: Part I, the critical regime and beyond, C.Erignoux, P. Gonçalves and G. Nahum, 26p, Journal of Statistical Physics, volume 181, pages 1433-1469, (2020)- [Bibitex/Bibitem Entries].

9. [EGN2020-2] Hydrodynamics for SSEP with non-reversible slow boundary dynamics: Part II, below the critical regime, C. Erignoux, P. Gonçalves and G. Nahum, 26p, ALEA volume 17, 791-823 (2020) - [Bibitex/Bibitem Entries].

10. [EG2020] Nematic first order phase transition for liquid crystals in the van der Waals-Kac limit, C. Erignoux and A. Giuliani, 18p, Journal of Mathematical Physics Vol.61, Issue 10 (2020) - [Bibitex/Bibitem Entries].

11. [BESS2020] Hydrodynamic limit for a facilitated exclusion process, O. Blondel, C. Erignoux, M. Sasada and M. Simon, 55p, Annales de l'IHP - Probabilités et Statistiques, Volume 56, Issue 1, pp 667-714 (2020) - [Bibitex/Bibitem Entries].

12. [ES2019] Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise, C.Erignoux and M. Simon, 54p, Electronic Journal of Probability, Vol. 24, n. 144 (2019) - [Bibitex/Bibitem Entries].

13. [E2018] Hydrodynamic limit of boundary driven exclusion processes with nonreversible boundary dynamics, C. Erignoux, 32p, Journal of Statistical Physics, Volume 172, Issue 5, pp 1327-1357 (2018) - [Bibitex/Bibitem Entries].

14. [KEBT2018] Exact Hydrodynamic description of active lattice gases, M. Kourbane- Houssene, C. Erignoux, T. Bodineau, J. Tailleur, 6p, Physics Review Letter, Vol. 120, 268003 (2018) - [Bibitex/Bibitem Entries].

15. [ELX2018] Stationary states of boundary driven exclusion processes with nonreversible boundary dynamics, C. Erignoux, C. Landim, T. Xu, 32p, Journal of Statistical Physics, Vol. 171, Issue 4, pp 599-631 (2018) - [Bibitex/Bibitem Entries].

• My PhD manuscript, Hydrodynamic Limit For An Active Lattice Gas

Lecture notes

• May 2-7 2022, IST Lisboa : lecture notes for my mini-course Varadhan's method for non gradient diffusive hydrodynamics, given to P. Gonçalves's probability group.

• KPZ universality conjectures and universality class, for a lecture for a BOUM-sponsored project with G. Barraquand, O. Blondel, et M. Simon.

Presentations and posters

A few presentations of my work

• A brief presentation of some of my research (30 minutes de Sciences, INRIA Lille, 2022)

• Stephan problem for kinetically constrained lattice gases (MODAL'X Seminar, Nanterre, 2021)

• Symmetric and asymmetric hydrodynamics for the FEP via mapping (Montreal University, 2022)

• Using duality to derive hydrodynamic and hydrostatic limits (IMPA, Rio de Janeiro, 2017)

• Scaling limits and behavior for microscopic stochastic models of active matter (Paris, 2021)

• A presentation of my PhD work (CAKE Seminar, Cambridge, 2016)

• A brief presentation of my work (CNRS Interviews, 2019)

• A brief presentation of our INRIA research group's work (INRIA Presentation, 2021)

Posters

Hydrodynamic Limit For An Active Lattice Gas, swarming and phase transitions, Presented to the COSMOS Workshop 2016