On Kac's chaos and related problems
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[1] E. Carlen. Superadditivity of Fisher's information and logarithmic Sobolev inequalities , 1991 .
[2] J. Doob. Stochastic processes , 1953 .
[3] P. Meyer,et al. Existence et unicité des représentations intégrales dans les convexes compacts quelconques , 1963 .
[4] Jo Graham,et al. Old and new , 2000 .
[5] A. Guillin,et al. Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation , 2009, 0906.1417.
[6] Elena Kosygina. THE BEHAVIOR OF THE SPECIFIC ENTROPY IN THE HYDRODYNAMIC SCALING LIMIT , 2001 .
[7] C. Bordenave,et al. Combinatorial Optimization Over Two Random Point Sets , 2011, 1103.2734.
[8] C. Villani. Optimal Transport: Old and New , 2008 .
[9] C. Villani,et al. Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality , 2000 .
[10] F. Otto. THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION , 2001 .
[11] Gennadiy P. Chistyakov,et al. Berry–Esseen bounds in the entropic central limit theorem , 2011, 1105.4119.
[12] G. Toscani,et al. Contractive Probability Metrics and Asymptotic Behavior of Dissipative Kinetic Equations , 2007 .
[13] F. Barthe,et al. Entropy of spherical marginals and related inequalities , 2006 .
[14] F. Grünbaum,et al. Propagation of chaos for the Boltzmann equation , 1971 .
[15] S. Varadhan,et al. Hydrodynamical limit for a Hamiltonian system with weak noise , 1993 .
[16] H. McKean. Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas , 1966 .
[17] C. Villani,et al. Entropy and chaos in the Kac model , 2008, 0808.3192.
[18] C. Villani. Topics in Optimal Transportation , 2003 .
[19] O. Lanford. Time evolution of large classical systems , 1975 .
[20] Pierre-Emmanuel Jabin,et al. N-particles Approximation of the Vlasov Equations with Singular Potential , 2003, math/0310039.
[21] Henry P. McKean,et al. The central limit theorem for Carleman’s equation , 1975 .
[22] Thierry Goudon,et al. Fourier-Based Distances and Berry-Esseen Like Inequalities for Smooth Densities , 2002 .
[23] P. Jabin,et al. Particles approximations of Vlasov equations with singular forces : Part. 2 , 2010 .
[24] Michel Talagrand,et al. Matching Random Samples in Many Dimensions , 1992 .
[25] J. Yukich,et al. Asymptotics for transportation cost in high dimensions , 1995 .
[26] R. Dudley. The Speed of Mean Glivenko-Cantelli Convergence , 1969 .
[27] L. J. Savage,et al. Symmetric measures on Cartesian products , 1955 .
[28] C. Villani,et al. Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces , 2005, math/0503123.
[29] F. G. Mehler. Ueber die Entwicklung einer Function von beliebig vielen Variablen nach Laplaceschen Functionen höherer Ordnung. , 1866 .
[30] DECREASE OF THE FISHER INFORMATION FOR SOLUTIONS OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION WITH MAXWELLIAN MOLECULES , 2000 .
[31] C. Villani,et al. Ricci curvature for metric-measure spaces via optimal transport , 2004, math/0412127.
[32] Gennadiy P. Chistyakov,et al. Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem , 2011, 1104.3994.
[33] W. Feller,et al. An Introduction to Probability Theory and Its Applications, Vol. II , 1972, The Mathematical Gazette.
[34] Horng-Tzer Yau,et al. Relative entropy and hydrodynamics of Ginzburg-Landau models , 1991 .
[35] H. McKean. An exponential formula for solving Boltzmann's equation for a Maxwellian gas* , 1967 .
[36] G. Toscani. New a priori estimates for the spatially homogeneous Boltzmann equation , 1992 .
[37] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .
[38] I. Fonseca,et al. Equilibrium configurations of defective crystals , 1992 .
[39] D. Freedman,et al. A dozen de Finetti-style results in search of a theory , 1987 .
[40] Feller William,et al. An Introduction To Probability Theory And Its Applications , 1950 .
[41] S. Bobkov,et al. Hypercontractivity of Hamilton-Jacobi equations , 2001 .
[42] Derek W. Robinson,et al. Mean entropy of states in classical statistical mechanics , 1967 .
[43] C. Chou. The Vlasov equations , 1965 .
[44] Thibaut Le Gouic,et al. On the mean speed of convergence of empirical and occupation measures in Wasserstein distance , 2011, 1105.5263.
[45] George Papanicolaou,et al. Nonlinear diffusion limit for a system with nearest neighbor interactions , 1988 .
[46] École d'été de probabilités de Saint-Flour,et al. Ecole d'été de probabilités de Saint-Flour XIX, 1989 , 1991 .
[47] A. C. Berry. The accuracy of the Gaussian approximation to the sum of independent variates , 1941 .
[48] Cédric Villani,et al. Fisher information estimates for Boltzmann's collision operator , 1998 .
[49] K. Carrapatoso. Propagation of chaos for the spatially homogeneous Landau equation for maxwellian molecules , 2012, 1212.3724.
[50] S. Méléard. Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models , 1996 .
[51] Emanuele Caglioti,et al. A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description , 1992 .
[52] Ofer Zeitouni,et al. Increasing propagation of chaos for mean field models , 1999 .
[53] Pierre-Louis Lions,et al. A Strengthened Central Limit Theorem for Smooth Densities , 1995 .
[54] Florent Malrieu,et al. Logarithmic Sobolev Inequalities for Some Nonlinear Pde's , 2001 .
[55] Dario Cordero-Erausquin,et al. Some Applications of Mass Transport to Gaussian-Type Inequalities , 2002 .
[56] A. Sznitman. Topics in propagation of chaos , 1991 .
[57] S. Rachev,et al. Mass transportation problems , 1998 .
[58] The homogeneous Boltzmann hierarchy and statistical solutions to the homogeneous Boltzmann equation , 1991 .
[59] A. Sznitman. Équations de type de Boltzmann, spatialement homogènes , 1984 .
[60] Hiroshi Tanaka,et al. Some probabilistic problems in the spatially homogeneous Boltzmann equation , 1983 .
[61] Nicolas Fournier,et al. Propagation of chaos for the 2D viscous vortex model , 2012, 1212.1437.
[62] Herbert Spohn,et al. Statistical mechanics of the isothermal lane-emden equation , 1982 .
[63] S. A.,et al. A Propagation of Chaos Result for Burgers ' Equation , 2022 .
[64] K. Carrapatoso. Quantitative and qualitative Kac's chaos on the Boltzmann's sphere , 2012, 1205.1241.
[65] János Komlós,et al. On optimal matchings , 1984, Comb..
[66] E. Lieb,et al. A sharp analog of Young’s inequality on SN and related entropy inequalities , 2004, math/0408030.
[67] Hirofumi Osada,et al. Propagation of chaos for the two dimensional Navier-Stokes equation , 1986 .
[68] B. D. Finetti. La prévision : ses lois logiques, ses sources subjectives , 1937 .
[69] C. Graham,et al. Stochastic particle approximations for generalized Boltzmann models and convergence estimates , 1997 .
[70] M. Kac. Foundations of Kinetic Theory , 1956 .
[71] Assaf Naor,et al. On the rate of convergence in the entropic central limit theorem , 2004 .
[72] E. Rio. Upper bounds for minimal distances in the central limit theorem , 2009 .