Justin Salez

Justin Salez

Contact

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)

Activities and links

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.

PhD students

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

Research papers

Entropy and curvature: beyond the Peres-Tetali conjecture (with F. Münch, P. Caputo). 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 K. Tikhomirov, P. Youssef). Journal of Functional Analysis, 285 (2023).
Separation cutoff for activated random walks (with A. Bristiel). 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 F. Münch). 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 J. Hermon). 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 J. Hermon). Annals of Applied Probability, 31 (2021).
Entropy dissipation estimates for inhomogeneous zero-range processes (with J. Hermon). Annals of Applied Probability, 31 (2021).
Emergence of extended states at zero in the spectrum of sparse random graphs (with S. Coste). Annals of Probability, 49 (2021).
Cutoff for the mean-field zero-range process with bounded monotone rates (with J. Hermon). 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 J. Hermon). Annals of Applied Probability, 29 (2019).
Cutoff for the mean-field zero-range process (with M. Merle). Annals of Probability, 47 (2019).
Cutoff at the "entropic time" for sparse Markov chains (with C. Bordenave, P. Caputo). Probability Theory and Related Fields, 173 (2019).
Random walk on sparse random digraphs (with C. Bordenave, P. Caputo). Probability Theory and Related Fields, 170 (2018).
Weighted sampling without replacement (with A. Ben-Hamou, Y. Peres). Brazilian Journal of Probability and Statistics, 32 (2018).
Cutoff for non-backtracking random walks on sparse random graphs (with A. Ben-Hamou). 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 V. Anantharam). Annals of Applied Probability, 26 (2016).
Cooperative strings and glassy interfaces (with T. Salez, K. Dalnoki-Veress, E. Raphael, J. Forrest). Proceedings of the National Academy of Sciences, 112 (2015).
The compulsive gambler process (with D. Aldous, D. Lanoue). 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 C. Bordenave, M. Lelarge). Probability Theory and Related Fields, 157 (2013).
The rank of diluted random graphs (with C. Bordenave, M. Lelarge). Annals of Probability, 39 (2011).
Belief propagation for the random assignment problem (with D. Shah). Mathematics of Operations Research, 34 (2009).
Optimality of belief propagation for the random assignment problem (with D. Shah). Proceedings of the 20th Symposium on Discrete Algorithms (2009).

Other writings

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).