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.

• Microscopic and macroscopic behavior and phase transitions for two-dimensional facilitated exclusion Processes, with M. Simon, A. Shapira and A. Roget.

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

• Cutoff phenomenon for the FEP's freezing time, with B. Massoulié.

• MIPS for a mixture of active and passive particles, with J. Mason, R. Jack and M. Bruna.

Submissions and preprints

• 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, Arxiv Preprint 2305.13853.

Publications

1. [BEL23] 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, Arxiv Preprint 2107.06606.

2. [MEJB23] 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, Nov. 2023, Arxiv Preprint 2307.11673.

3. [E2023] On the hydrodynamics of active matter models on a lattice, C. Erignoux, 18p, To appear in Markov Processes and Related Fields - IRS proceedings, , Arxiv Preprint 2108.04003.

4. [ESZ2023] Mapping hydrodynamics for the facilitated exclusion and zero-range processes, C. Erignoux, M. Simon and L. Zhao, 45p, To appear in Annals of Applied Probability, , Arxiv Preprint 2202.04469.

5. [ESZ2023-1] 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), Arxiv Preprint 2109.04133 - [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), Arxiv Preprint 1912.09583 - [Bibitex/Bibitem Entries].

7. [E2021] Hydrodynamic limit for an active exclusion process, C.Erignoux, 214p, Mémoires de la SMF, Volume 169 (2021), Arxiv Preprint 1608.04937 - [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), Arxiv Preprint 1912.09841 - [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 v.17, 791-823 (2020) Arxiv Preprint 1912.09842 - [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) Arxiv Preprint 2002.12875 - [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) Arxiv Preprint 1805.09000 - [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) Arxiv Preprint 1402.3617 - [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) Arxiv Preprint 1712.04877 - [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) Arxiv Preprint 1801.08952 - [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) Arxiv Preprint 1711.06201 - [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