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This is a survey of recent developments in the area of transport inequalities.
Information and information stability of random variables and processes
M. Pinsker · 1964
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Information-type measures of difference of probability distributions and indirect observations
I. Csiszár · 1967
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A lower bound for discrimination information in terms of variation
S. Kullback · 1967
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The description of a random field by means of conditional probabilities and condition of itd regularity
R. Dobrushin · 1968
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Prescribing a system of random variables by conditional distributions
R. Dobrushin · 1970
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On a certain converse of Hölder’s inequality
L. Leindler · 1972
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Hardy’s inequality with weights
B. Muckenhoupt · 1972
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On logarithmic concave measures and functions
A. Prékopa · 1973
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Asymptotic evaluations of certain Markov process expectations for large time, I
M. Donsker and S. Varadhan · 1975
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A topological application of the isoperimetric inequality
M. Gromov and V.D. Milman · 1983
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On the optimal mapping of distributions
M. Knott and C. Smith · 1984
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Diffusions hypercontractives
D. Bakry and M. Emery · 1985
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A simple proof of the blowing-up lemma
K. Marton · 1986
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Random fields and diffusion processes, in Ecole d’Eté de Probabilités de Saint-Flour XV-XVII-1985-87
H. Föllmer · 1988
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A generalized Poincaré inequality for Gaussian measures
W. Beckner · 1989
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Large Deviations
J-D. Deuschel and D. Stroock · 1989
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Polar factorization and monotone rearrangement of vector-valued functions
Y. Brenier · 1991
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Superadditivity of Fisher’s information and logarithmic Sobolev inequalities
E. Carlen · 1991
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Topics in matrix analysis
R. A. Horn and C. R. Johnson · 1991
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Some deviation inequalities
B. Maurey · 1991
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The equivalence between the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition
D. Stroock and B. Zegarlinski · 1992
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The logarithmic Sobolev inequality for discrete spin systems on the lattice
D. Stroock and B. Zegarlinski · 1992
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Dobrushin uniqueness theorem and logarithmic Sobolev inequalities
B. Zegarlinski · 1992
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A convexity theory for interacting gases and equilibrium crystals
R. McCann · 1994
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Isoperimetric problems for convex bodies and a localization lemma
R. Kannan, L. Lovász, and M. Simonovits · 1995
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Existence and uniqueness of monotone measure-preserving maps
R. McCann · 1995
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Concentration of measure and isoperimetric inequalities in product spaces
M. Talagrand · 1995
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Transportation approach to some concentration inequalities in product spaces
A. Dembo and O. Zeitouni · 1996
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The geometry of optimal transportation
W. Gangbo and R. McCann · 1996
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On Talagrand’s deviation inequalities for product measures
M. Ledoux · 1996
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Bounding d ¯ \overline{d} -distance by informational divergence: a method to prove measure concentration
K. Marton · 1996
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A measure concentration inequality for contracting Markov chains
K. Marton · 1996
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New concentration inequalities in product spaces
M. Talagrand · 1996
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A new look at independence
M. Talagrand · 1996
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Transportation cost for Gaussian and other product measures
M. Talagrand · 1996
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Inégalités fonctionnelles et géométriques obtenues par transport de mesures
F. Barthe · 1997
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Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy
G. Ben Arous and A. Guionnet · 1997
Earlier work this paper cites.
Isoperimetric constants for product probability measures
S. Bobkov and C. Houdré · 1997
Cited alongside, same era.
Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution
S. Bobkov and M. Ledoux · 1997
Cited alongside, same era.
Information inequalities and concentration of measure
A. Dembo · 1997
Cited alongside, same era.
Lectures on Glauber dynamics for discrete spin models
F. Martinelli · 1997
Cited alongside, same era.
Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
F-Y. Wang · 1997
Cited alongside, same era.
On a reverse form of the brascamp-lieb inequality
F. Barthe · 1998
Cited alongside, same era.
Entropy bounds and isoperimetry
S. Bobkov and B. Zegarlinski · 2005
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Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
F. Bolley and C. Villani · 2005
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Modified logarithmic Sobolev inequalities and transportation inequalities
I. Gentil, A. Guillin, and L. Miclo · 2005
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A (one-dimensional) free Brunn-Minkowski inequality
M. Ledoux · 2005
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A generalization of Poincaré and log-Sobolev inequalities
F-Y. Wang · 2005
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Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
F. Barthe, P. Cattiaux, and C. Roberto · 2006
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Large deviations techniques and applications. Second edition
A. Dembo and O. Zeitouni · 1998
Cited alongside, same era.
Measure concentration for a class of random processes
K. Marton · 1998
Cited alongside, same era.
Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
S. Bobkov and F. Götze · 1999
Cited alongside, same era.
Une initiation aux inégalités de Sobolev logarithmiques
G. Royer · 1999
Cited alongside, same era.
Sur les inégalités de Sobolev logarithmiques
C. Ané, S. Blachère, D. Chafaï, P. Fougères, I. Gentil, F. Malrieu, C. Roberto, and G. Scheffer · 2000
Cited alongside, same era.
From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
S. Bobkov and M. Ledoux · 2000
Cited alongside, same era.
Talagrand’s like quadratic transportation cost inequalities
P. Cattiaux and A. Guillin · 2006
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Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
D. Cordero-Erausquin, R. McCann, and M. Schmuckenschläger · 2006
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Integral criteria for transportation cost inequalities
N. Gozlan · 2006
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Large random matrices: lectures on macroscopic asymptotics
A. Guionnet · 2006
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Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition
L. Wu · 2006
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Transportation-information inequalities for Gibbs measures
F. Gao and L. Wu · 2007
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Characterization of Talagrand’s like transportation-cost inequalities on the real line
N. Gozlan · 2007
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A large deviation approach to some transportation cost inequalities
N. Gozlan and C. Léonard · 2007
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Hamilton-Jacobi semigroup on length spaces and applications
J. Lott and C. Villani · 2007
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Talagrand inequality for the semicircular law and energy of the eigenvalues of beta ensembles
I. Popescu · 2007
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Infimum-convolution description of concentration properties of product probability measures, with applications
P-M Samson · 2007
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A simple proof of the Poincaré inequality for a large class of probability measures including the log-concave case
D. Bakry, F. Barthe, P. Cattiaux, and A. Guillin · 2008
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Mass transport and variants of the logarithmic Sobolev inequality
F. Barthe and A. V. Kolesnikov · 2008
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Modified logarithmic Sobolev inequalities on ℝ \mathbb{R}
F. Barthe and C. Roberto · 2008
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A note on Talagrand transportation inequality and logarithmic Sobolev inequality
P. Cattiaux, A. Guillin, and L-M. Wu · 2008
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Poincaré inequality and dimension free concentration of measure
N. Gozlan · 2008
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A. Guillin, C. Léonard, F. Wang, and L. Wu · 2008
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On the infimum convolution inequality
R. Latała and J. Wojtaszczyk · 2008
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From super Poincaré to weighted log-Sobolev and entropy-cost inequalities
F-Y. Wang · 2008
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Generalized transportation-cost inequalities and applications
F-Y. Wang · 2008
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Bernstein type’s concentration inequalities for symmetric Markov processes
F. Gao, A. Guillin, and L. Wu · 2009
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A characterization of dimension free concentration in terms of transport inequalities
N. Gozlan · 2009
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A refined version of Otto and Villani theorem
N. Gozlan, C. Roberto, and P-M. Samson · 2009
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Transportation-information inequalities for Markov processes
A. Guillin, C. Léonard, L. Wu, and N. Yao · 2009
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Mass transportation proofs of free functional inequalities, and free Poincaré inequalities
M. Ledoux and I. Popescu · 2009
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Isoperimetric and concentration inequalities - part i: Equivalence under curvature lower bound
E. Milman · 2009
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On the role of convexity in functional and isoperimetric inequalities
E. Milman · 2009
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On the role of convexity in isoperimetry, spectral gap and concentration
E. Milman · 2009
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Optimal transport
C. Villani · 2009
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Transportation inequalities for stochastic differential equations of pure jumps
L. Wu · 2009
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An Introduction to Random Matrices
G. Anderson, A. Guionnet, and O. Zeitouni · 2010
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