Bounds on optimal transport maps onto log-concave measures

Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math

1991

Earlier work this paper cites.

R. Kannan, L. Lovász and M. Simonovits, Isoperimetric problems for convex bodies and a localization lemma. Discrete Comput. Geom

1995

Earlier work this paper cites.

L.A. Caffarelli, Monotonicity Properties of Optimal Transportation and the FKG and Related Inequalities, Communications in Mathematical Physics

2000

Earlier work this paper cites.

D. Cordero-Erausquin, Some applications of mass transport to Gaussian type inequalities, Arch. Rational Mech. Anal

2002

Earlier work this paper cites.

D. Cordero-Erausquin, M. Fradelizi and B. Maurey, The (B)-conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems, J. Funct. Anal

2004

Earlier work this paper cites.

G. Paouris, Concentration of mass on convex bodies. Geometric and Functional Analysis

2006

Earlier work this paper cites.

E. Milman, On the role of convexity in isoperimetry, spectral gap and concentration, Invent. Math

2009

Earlier work this paper cites.

O. Guedon and E. Milman. Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures. Geometric and Functional Analysis

2011

Earlier work this paper cites.

A. Kolesnikov, Mass transportation and contractions. Arxiv preprint

2011

Cited alongside, same era.

Y.-H. Kim and E. Milman, A Generalization of Caffarelli’s Contraction Theorem via (reverse) Heat Flow, Math. Annal

2012

Cited alongside, same era.

R. Eldan, Thin shell implies spectral gap via a stochastic localization scheme. Geom. Funct. Anal

2013

Cited alongside, same era.

Kolesnikov A. On Sobolev Regularity of Mass Transport and Transportation Inequalities. Theory of Probability and Its Applications

2013

Cited alongside, same era.

B. Klartag and A. Kolesnikov, Eigenvalue distribution of optimal transportation. Anal. PDE

2015

Cited alongside, same era.

M. Colombo, Y. Jhaveri and A. Figalli, Lipschitz changes of variables between perturbations of log-concave measures Ann. Sc. Norm. Super. Pisa Cl. Sci

D. Cordero-Erausquin and A. Figalli, Regularity of monotone maps between unbounded domains. Discrete Contin. Dyn. Syst., to appear

2018

Later among the works it cites.

T. Courtade, M. Fathi and A. Pananjady, Quantitative stability of the entropy power inequality. IEEE Trans. Inform. Theory

2018

Later among the works it cites.

Y.T. Lee and S. Vempala, Stochastic Localization + Stieltjes Barrier = Tight Bound for Log-Sobolev. STOC 2018

2018

Later among the works it cites.

Y.T. Lee and S. Vempala, The Kannan-Lovász-Simonovits Conjecture. Arxiv preprint

2018

Later among the works it cites.

E. Milman, Spectral Estimates, Contractions and Hypercontractivity, J. Spectr. Theory

2018

Later among the works it cites.