Fetching the paper…
Reading the bibliography…
We develop connections between Stein's approximation method, logarithmic Sobolev and transport inequalities by introducing a new class of functional inequalities involving the relative entropy, the Stein kernel, the relative Fisher information and the Wasserstein distance with respect to a given reference distribution on $\mathbb{R}^d$.
A. Stam (1959). Some inequalities satisfied by the quantities of information of Fisher and Shannon
1959
Earlier work this paper cites.
N. Blachman (1965). The convolution inequality for entropy powers
1965
Earlier work this paper cites.
J.-M. Bismut (1984)
1984
Earlier work this paper cites.
D. Bakry, M. Émery (1985). Diffusions hypercontractives. Séminaire de Probabilités XIX, Lecture Notes in Math
1985
Earlier work this paper cites.
C. Stein (1986)
1986
Earlier work this paper cites.
A. D. Barbour (1990). Stein’s method for diffusion approximations
1990
Earlier work this paper cites.
P. Diaconis, S. Zabell (1991). Closed form summation for classical distributions: variations on a theme of de Moivre
1991
Earlier work this paper cites.
F. Götze (1991). On the rate of convergence in the multivariate CLT
1991
Earlier work this paper cites.
T. Cacoullos, V. Papathanasiou, S. Utev (1994). Variational inequalities with examples and an application to the central limit theorem
1994
Earlier work this paper cites.
M. Ledoux (1995). L’algèbre de Lie des gradients itérés d’un générateur markovien—développements de moyennes et entropies
1995
Earlier work this paper cites.
M. Talagrand (1996). Transportation cost for Gaussian and other product measures
1996
Earlier work this paper cites.
L. Goldstein, G. Reinert (1997). Stein’s method and the zero bias transformation with application to simple random sampling
1997
Earlier work this paper cites.
F. Otto, C. Villani (2000). Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality
2000
Earlier work this paper cites.
A. Carbery, J. Wright (2001). Distributional and
2001
Earlier work this paper cites.
M. Ledoux (2001)
2001
Cited alongside, same era.
S. Artstein, K. Ball, F. Barthe, A. Naor (2004). On the rate of convergence in the entropic central limit theorem
2004
Cited alongside, same era.
A. Barron, O. Johnson (2004). Fisher information inequalities and the central limit theorem
2004
Cited alongside, same era.
Information theory and the central limit theorem
O. Johnson (2004) · 2004
Cited alongside, same era.
L. Goldstein, G. Reinert (2005). Zero biasing in one and higher dimensions, and applications. Stein’s method and applications, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 5, 1–18. Singapore Univ. Press
2005
Cited alongside, same era.
G. Reinert (2005). Three general approaches to Stein’s method. An introduction to Stein’s method, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 4, 183–221. Singapore Univ. Press
S. Chatterjee (2012). A new approach to strong embeddings
2012
Later among the works it cites.
M. Ledoux (2012). Chaos of a Markov operator and the fourth moment condition
2012
Later among the works it cites.
Normal approximations with Malliavin calculus: from Stein’s method to universality
I. Nourdin, G. Peccati (2012) · 2012
Later among the works it cites.
E. Azmoodeh, S. Campese, G. Poly (2013). Fourth moment theorems for Markov diffusion generators
2013
Later among the works it cites.
E. Azmoodeh, D. Malicet, G. Poly (2013). Generalization of the Nualart-Peccati criterion
2013
Later among the works it cites.
S. Bobkov, G. Chistyakov, F. Götze (2013). Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem
2013
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2005
Cited alongside, same era.
D. Nualart, D. (2006)
2006
Cited alongside, same era.
S. Chatterjee (2007). Stein’s method for concentration inequalities
2007
Cited alongside, same era.
S. Chatterjee (2009). Fluctuation of eigenvalues and second order Poincaré inequalities
2009
Cited alongside, same era.
E. Milman (2009). On the role of convexity in isoperimetry, spectral gap and concentration
2009
Cited alongside, same era.
I. Nourdin, G. Peccati (2009). Non-central convergence of multiple integrals
2009
Cited alongside, same era.
C. Villani (2009)
2009
Cited alongside, same era.
Later among the works it cites.
S. Bobkov, G. Chistyakov, F. Götze (2013) Berry-Esseen bounds in the entropic central limit theorem
2013
Later among the works it cites.
S. Boucheron, G. Lugosi, P. Massart (2013)
2013
Later among the works it cites.
I. Nourdin, G. Peccati, Y. Swan (2013). Entropy and the fourth moment phenomenon
2013
Later among the works it cites.
I. Nourdin, G. Peccati, Y. Swan (2013). Integration by parts and representation of information functionals. Preprint
2013
Later among the works it cites.
D. Bakry, I. Gentil, M. Ledoux (2014)
2014
Closest in time.
S. Bobkov, G. Chistyakov, F. Götze (2014). Fisher information and the central limit theorem
2014
Closest in time.
L. Mackey, M. I. Jordan, R. Y. Chen, B. Farrell, J. A. Tropp (2014). Matrix concentration inequalities via the method of exchangeable pairs
2014
Closest in time.