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We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension.
Henstock, R., Macbeath, A. M., On the measure of sum-sets. I. The theorems of Brunn, Minkowski, and Lusternik
1953
Earlier work this paper cites.
Knothe, H., Contributions to the theory of convex bodies
1957
Earlier work this paper cites.
Cheeger, J., A lower bound for the smallest eigenvalue of the Laplacian
1970
Earlier work this paper cites.
Bakry, D., Émery, M., Diffusions hypercontractives
1985
Earlier work this paper cites.
Milman, V. D., Schechtman, G., Asymptotic theory of finite-dimensional normed spaces
1986
Earlier work this paper cites.
Brenier, Y., Polar factorization and monotone rearrangement of vector-valued functions
1991
Earlier work this paper cites.
Talagrand, M., Concentration of measure and isoperimetric inequalities in product spaces
1995
Earlier work this paper cites.
Dembo, A., Zeitouni, O., Transportation approach to some concentration inequalities in product spaces
1996
Earlier work this paper cites.
Marton, K., A measure concentration inequality for contracting Markov chains
1996
Cited alongside, same era.
Talagrand, M., Transportation cost for Gaussian and other product measures
1996
Cited alongside, same era.
Barthe, F., Inégalités de Brascamp-Lieb et convexité
1997
Cited alongside, same era.
Ledoux, M., On Talagrand’s deviation inequalities for product measures
1997
Cited alongside, same era.
McCann, R. J., A convexity principle for interacting gases
1997
Cited alongside, same era.
Barthe, F., On a reverse form of the Brascamp-Lieb inequality
1998
Cited alongside, same era.
Cordero-Erausquin, D., Some applications of mass transport to Gaussian-type inequalities
2002
Later among the works it cites.
Villani, C., Topics in optimal transportation
2003
Later among the works it cites.
Klartag, B., Marginals of geometric inequalities
2007
Later among the works it cites.
Royer, G., An initiation to logarithmic Sobolev inequalities
2007
Later among the works it cites.
Klartag, B., A Berry-Esseen type inequality for convex bodies with an unconditional basis
2009
Later among the works it cites.
Leoni, G., A first course in Sobolev spaces
2009
Later among the works it cites.
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1999
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Otto, F., Villani, C., Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
2000
Cited alongside, same era.
Eldan, R., Klartag, B., Dimensionality and the stability of the Brunn-Minkowski inequality
Cited in the paper.
2010
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Milman, E., Isoperimetric and concentration inequalities - equivalence under curvature lower bound
2010
Later among the works it cites.