Welcome to my page! I am a professor of Mathematics at Université Paris-Dauphine & PSL, and a member of CEREMADE.
**Address:** Université Paris-Dauphine - CEREMADE, Place du Maréchal de Lattre de Tassigny, F-75775 Paris Cedex 16, FRANCE

**Office:** P209TER

**e-mail:** FIRST.LAST@dauphine.psl.eu (with FIRST=justin and LAST=salez)

- I am the principal investigator of the ERC project CUTOFF.
- I am a member of the ANR project Conviviality.
- I am a junior fellow of Institut Universitaire de France.
- I am an associate editor of ECP-EJP.
- I teach the Master's course Introduction to stochastic calculus.
- I teach the Master's course Mixing times of Markov chains.
- I co-organize our monthly Colloquium.

- Alexandre Bristiel (in progress).
- Hong Quan Tran (in progress).
- Guillaume Conchon-Kerjan (2021).
- Simon Coste (2019), co-advised with .
- Anna Ben-Hamou (2016), co-advised with .

- Entropy and curvature: beyond the Peres-Tetali conjecture (with , ). Submitted (2024).
- The varentropy criterion is sharp on expanders.
*Annales Henri Lebesgue*, to appear. - Spectral gap and curvature of monotone Markov chains.
*Annals of Probability*, to appear. - Upgrading MLSI to LSI for reversible Markov chains (with
, ).
*Journal of Functional Analysis*,**285**(2023). - Separation cutoff for activated random walks (with ). Submitted (2022).
- Cutoff for non-negatively curved Markov chains.
*Journal of the European Mathematical Society*, to appear. - Mixing time and expansion of non-negatively curved Markov chains (with
).
*Journal de l'École polytechnique*,**10**(2023). - Universality of cutoff for exclusion with reservoirs.
*Annals of Probability*,**51**(2023). - Modified log-Sobolev inequalities for strong-Rayleigh measures
(with
).
*Annals of Applied Probability*,**33**(2023). - Sparse expanders have negative curvature.
*Geometric and Functional Analysis*,**32**(2022). - A sharp log-Sobolev inequality for the multislice.
*Annales Henri Lebesgue*,**4**(2021). - The interchange process on high-dimensional products
(with
).
*Annals of Applied Probability*,**31**(2021). - Entropy dissipation estimates for inhomogeneous zero-range processes
(with
).
*Annals of Applied Probability*,**31**(2021). - Emergence of extended states at zero in the spectrum of sparse random graphs
(with
).
*Annals of Probability*,**49**(2021). - Cutoff for the mean-field zero-range process with bounded monotone rates
(with
).
*Annals of Probability*,**48**(2020). - Spectral atoms of unimodular random trees.
*Journal of the European Mathematical Society*,**22**(2020). - A version of Aldous' spectral-gap conjecture for the zero range process
(with
).
*Annals of Applied Probability*,**29**(2019). - Cutoff for the mean-field zero-range process
(with
).
*Annals of Probability*,**47**(2019). - Cutoff at the "entropic time" for sparse Markov chains
(with
,
).
*Probability Theory and Related Fields*,**173**(2019). - Random walk on sparse random digraphs
(with
,
).
*Probability Theory and Related Fields*,**170**(2018). - Weighted sampling without replacement
(with
,
).
*Brazilian Journal of Probability and Statistics*,**32**(2018). - Cutoff for non-backtracking random walks on sparse random graphs
(with ).
*Annals of Probability*,**45**(2017). - The interpolation method for random graphs with prescribed degrees.
*Combinatorics, Probability and Computing*,**25**(2016). - The densest subgraph problem in sparse random graphs
(with ).
*Annals of Applied Probability*,**26**(2016). - Cooperative strings and glassy interfaces
(with , , , ).
*Proceedings of the National Academy of Sciences*,**112**(2015). - The compulsive gambler process
(with , ).
*Electronic Journal of Probability*,**20**(2015). - The Mézard-Parisi equation for matchings in pseudo-dimension d>1.
*Electronic Communications in Probability*,**20**(2015). - Every totally real algebraic integer is a tree eigenvalue.
*Journal of Combinatorial Theory, series B*,**111**(2015). - Joint distribution of distances in large random regular networks.
*Journal of Applied Probability*,**50**(2013). - Weighted enumeration of spanning subgraphs in locally tree-like graphs.
*Random Structures and Algorithms*,**43**(2013). - Matchings on infinite graphs
(with
,
).
*Probability Theory and Related Fields*,**157**(2013). - The rank of diluted random graphs
(with , ).
*Annals of Probability*,**39**(2011). - Belief propagation for the random assignment problem
(with
).
*Mathematics of Operations Research*,**34**(2009). - Optimality of belief propagation for the random assignment problem
(with ).
*Proceedings of the 20th Symposium on Discrete Algorithms*(2009).

- Mixing times of Markov chains. Lecture notes (2022).
- Introduction to stochastic calculus. Lecture notes (2022).
- Spectra of sparse random graphs. Lecture notes (2019).
- Sparse random graphs: structure & dynamics. Habilitation thesis (2016).
- Some implications of local weak convergence for large random graphs. PhD thesis (2011).