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Publications


Preprints
C. Léonard, R. Mohayaee. Monge-Ampère gravitating fluids. Least action principles and particle systems. PDF 
A. Baradat, C. Léonard. Minimizing relative entropy of path measures under marginal constraints. (not submitted yet)  PDF 
C. Léonard. Revisiting Fortet's proof of existence of a solution to the Schrödinger system. (not to be published)  
Papers P. Cattiaux, G. Conforti, I. Gentil and C. Léonard. Time reversal of diffusion processes under a finite entropy condition. Annales de l'Institut Henri Poincaré Probab. Statist.59(4), 1844-1881, (2023)    PDF    
C. Léonard. Feynman-Kac formula under a finite entropy condition.  Probability Theory and Related Fields 184, 1029-1091, (2022)  PDF            
G. Conforti and C. Léonard. Time reversal of Markov processes with jumps under a finite entropy condition.  Stochastic Processes and their Applications 144, 85-124, (2022)  PDF       
J. Backhoff, G. Conforti, I. Gentil, C. Léonard. The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities.  Probability Theory and Related Fields. 178,  475–530 (2020)   PDF 
M. Arnaudon, A.B. Cruzeiro, C. Léonard, J.-C. Zambrini. An entropic interpolation problem for incompressible viscid fluids. Annales de l'Institut Henri Poincaré Probab. Statist. 56(3), 2211-2235, (2020)  pdf  arXiv
I. Gentil, C. Léonard, L. Ripani and L.Tamanini. An entropic interpolation proof of the HWI inequality. Stochastic Processes and their Applications. 130(2), 907-923 (2020)  pdf  arXiv  
I. Gentil, C. Léonard and L. Ripani. Dynamical aspects of generalized Schrödinger problem via Otto calculus - A heuristic point of view. Revista Matemática Iberoamericana , online version, 36(4), 1071–1112 (2020)  pdf  arXiv
C. Léonard. On the convexity of the entropy along entropic interpolations. In: Measure Theory in Non-Smooth Spaces, (ed. N. Gigli), Partial Differential Equations and Measure Theory. De Gruyter Open, June 2017, 195-242.  PDF  arxiv
G. Conforti and C. Léonard. Reciprocal classes of random walks on graphs.  Stoch. Proc. Appl., 27(6), 1870-1896, (2017).  PDF 
I. Gentil, C. Léonard and L. Ripani. About the analogy between optimal transport and minimal entropy. Ann. Fac. Toulouse, Série 6, Vol.26 (3), 569-600 (2017).  PDF 
C. Léonard. Lazy random walks and optimal transport on graphs, Ann. Probab., 44(3), (2016), 1864-1915.  PDF 
C. Léonard. Some geometric consequences of the Schrödinger problem. Geometric Science of Information. Proceedings of the Second International Conference, GSI 2015. Lecture Notes in Computer Science, Vol. 9389 (2015), pp. 60-68.  PDF  HAL
G. Conforti, C. Léonard, R. Murr and S. Roelly. Bridges of Markov counting processes. Reciprocal classes and duality formulas. Electr. Comm. Probab., Vol. 20, Article 18, (2015), 12 pp.  PDF 
C. Léonard, S. Roelly and J.-C. Zambrini. Reciprocal processes. A measure-theoretical point of view, Probability Surveys 2014, Vol. 11, 237-269.  PDF 
M. Klein, C. Léonard and E. Rosenberger. Agmon-type estimates for a class of jump processes, Math. Nachr. 287, No. 17–18, 2021–2039 (2014).  PDF 
  • C. Léonard. Some properties of path measures, Séminaire de probabilités 46. Lecture Notes in Mathematics 2123 (2014), pp 207-230.  PDF 
  • E. Boissard, N. Gozlan, J. Lehec, C. Léonard, G. Menz, A. Schlichting. Some recent developments in functional inequalities. Journées MAS 2012. ESAIM: Proc. 44, 338-354 (2014).  PDF  HAL
  • M. Beiglböck, C. Léonard and W. Schachermayer. On the duality for the Monge-Kantorovich transport problem, London Mathematical Society Lecture Notes Series, 413, (2014).  PDF 
  • C. Léonard. A survey of the Schrödinger problem and some of its connections with optimal transport, Discrete Contin. Dyn. Syst. A, 2014, 34(4): 1533-1574.  PDF 
  • M. Beiglböck, C. Léonard and W. Schachermayer. A general duality theorem for the Monge-Kantorovich transport problem,  Studia Math. 209 (2012), 151-16.  PDF 
  • M. Beiglböck, C. Léonard and W. Schachermayer. A generalized dual maximizer for the Monge-Kantorovich transport problem, ESAIM P&S, 2012 (16), 306-323.  PDF 
  • C. Léonard. Girsanov theory under a finite entropy condition. Séminaire de probabilités, vol. 44. Lecture Notes in Mathematics 2046, Springer-Verlag, 2012, 429-465.  PDF 
  • C. Léonard. From the Schrödinger problem to the Monge-Kantorovich problem.  J. Funct. Anal, 2012, 262: 1879–1920.  PDF 
  • C. Léonard. A saddle-point approach to the Monge-Kantorovich optimal transport problem. ESAIM COCV, July 2011, 17 : pp 682-704.  PDF 
  • C. Léonard. Entropic projections and dominating points. ESAIM P&S, 14, December 2010, 343-381.  PDF 
  • N. Gozlan and C. Léonard. Transport inequalities. A survey. Markov Processes and Related Fields, 16, 2010, 635-736.  PDF 
  • C. Léonard and J-C. Zambrini. A probabilistic deformation of calculus of variations with constraints, Seminar on stochastic analysis, random fields and applications, VI. (Ascona, 2008). Progress in Probability, vol. 63, 177-189. (Birkhaüser), 2010.  PDF 
  • C. Léonard. Convex minimization problems with weak constraint qualifications. Journal of Convex Analysis, 17 (1), 2010, 321-348.  PDF 
  • A. Guillin, C. Léonard, L. Wu and N. Yao. Transportation-information inequalities for Markov processes. Probability Theory and Related Fields, 2009, 144:669–695.  PDF 
  • C. Léonard. Minimization of entropy functionals, J. Math. Anal. Appl. 346, 2008, 183–204.  PDF 
  • N. Gozlan and C. Léonard. A large deviation approach to some transportation cost inequalities. Probability Theory and Related Fields. Vol. 139,  2007, 235-283.  PDF 
  • C. Léonard. Minimizers of energy functionals under not very integrable constraints. Journal of Convex Analysis. 10 (1), 2003, 63-88.  PDF  
  • S. Boucheron, F. Gamboa and C. Léonard. Bins and balls : Large deviations of the empirical occupancy process. The Annals of Applied Probability. 12, 2002, 607-636.  PDF  
  • C. Léonard and J. Najim. An extension of Sanov’s theorem. Application to the Gibbs conditioning principle. Bernoulli. Vol.8(6),  2002, 721-743.  PDF  
  • C. Léonard. Minimizers of energy functionals.  Acta Math. Hungar. 93 (4), 2001, 281-325.  PDF  
  • C. Léonard. Convex conjugates of integral functionals.  Acta Math. Hungar. 93 (4), 2001, 253-280.  PDF  
  • C. Léonard. Minimization of energy functionals applied to some inverse problems. J. App. Math. Optim. 44, 2001, 273-297.  PDF  
  • C. Léonard. Some results about entropic projections, in "Stochastic Analysis and Mathematical Physics ”, Birkhäuser, Progress in Probability, Vol. 50, (2001).  PDF  
  • C. Léonard. Large deviations for Poisson random measures and processes with independent increments. Stochastic Processes and their Applications. 85, (2000), 93-121.  PDF  
  • P. Cattiaux, C. Léonard. Minimization of the Kullback information for some Markov processes, Séminaire de Probabilité XXX, Lecture Notes in Mathematics 1626, (1996), 288-311.  PDF  Mathdoc 
  • P. Cattiaux, C. Léonard. Large deviations and Nelson processes, Forum Math. 7 (1995), 95-115.  PDF  
  • C. Kipnis, C. Léonard. Grandes déviations pour un système hydrodynamique asymétrique de particules indépendantes,  Ann. Inst. Henri  Poincaré, (In Memoriam C. Kipnis), Vol. 31, No 1, (1995), 223-248.    PDF  Mathdoc
  • C. Léonard. Large deviations for particle systems associated with spatially homogeneous Boltzmann type equations, Prob. Th. Rel. Fields, Vol. 101, No 1, (1995), 1-44.  PDF 
  • C. Léonard. Large deviations for long range interacting particle systems with jumps, Ann. Inst. Henri Poincaré, Vol. 31, No 2, (1995), 289-323.  PDF  Mathdoc 
  • P. Cattiaux, C. Léonard. Minimization of the Kullback information of diffusion processes, Ann. Inst. Henri  Poincaré, Vol. 30, No 1, (1994), 83-132. PDF  Mathdoc  , with an erratum at  PDF   Mathdoc
  • C. Léonard. Large deviations and Boltzmann equation, in CRM Proceedings and Lecture Notes, "Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems", Ed: D. A. Dawson, Montréal, (1994), 165-174.  
  • C. Léonard. Some epidemic systems are long range interacting particle systems, in Stochastic processes in epidemic theory. Lecture Notes in Biomathematics, n°86, (1990), 170-183. PDF
  • C. Léonard. Large deviations and law of large numbers for a mean field type interacting particle system. Stoch. Proc. and their Appl.,  Vol.25, No 2, (1987), 215-235.  
  • C. Léonard. Une loi des grands nombres pour des systèmes de diffusion avec interaction et à coefficients non bornés, Ann. Inst. Henri Poincaré, Vol. 22, No 2, (1986), 237-262.  Mathdoc

ThesesThèse de doctorat d'état : "Quelques problèmes de grandes déviations", (Some large deviations problems). Université Paris-Sud Orsay, (1991).

PhD Thesis: "Sur la limite en loi et les fluctuations de certains modèles dynamiques d'interaction", (On the weak limit and fluctuations of some interacting dynamical random systems). Université Paris-Sud Orsay, (1984).


Lecture notesA first draft of my lecture notes on convex optimization with an application to optimal transport, May 2006.  PDF
Some notes on Orlicz spaces, April 2007. PDF

My co-authors
Click here to see the list of my co-authors with links to their websites

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