Fetching the paper…
Reading the bibliography…
We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.
1901
Earlier work this paper cites.
Lieb, E. H. Some convexity and subadditivity properties of entropy. Bull. Amer. Math. Soc. 81 (1975), 1–13
1975
Earlier work this paper cites.
Barron, A. R. Entropy and the central limit theorem. Ann. Probab. 14, (1986), no. 1, 336–342
1986
Earlier work this paper cites.
Bourgain, J. On high-dimensional maximal functions associated to convex bodies. Amer. J. Math. 108 (1986), no. 6, 1467–1476
1986
Earlier work this paper cites.
Massey, J. L. On the entropy of integer-valued random variables. In: Proc. 1988 Beijing Int. Workshop on Information Theory, pages C1.1-C1.4, July 1988
1988
Earlier work this paper cites.
Rudin, W. Functional analysis. Second edition. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, 1991. xviii+424 pp
1991
Earlier work this paper cites.
Talagrand, M. Transportation cost for Gaussian and other product measures. Geom. Funct. Anal. 6 (1996), no. 3, 587–600
1996
Earlier work this paper cites.
Miclo, L. Notes on the speed of entropic convergence in the central limit theorem. Stochastic inequalities and applications, Birkhäuser, Basel. Progr. Probab, 56:129–156, 2003
2003
Earlier work this paper cites.
Villani, C. Topics in optimal transportation. Graduate Studies in Mathematics, 58. American Mathematical Society, Providence, RI, 2003. xvi+370 pp
2003
Earlier work this paper cites.
Artstein, S.; Ball, K.; Barthe, F.; Naor, A. On the rate of convergence in the entropic central limit theorem. Probab. Theory Related Fields 129 (2004), no. 3, 381–390
2004
Cited alongside, same era.
Harremoës, P.; Vignat, C. A short information theoretic proof of CLT. Preprint (2004). Available at http://www-syscom.univ-mlv.fr/ vignat/Signal/CLT.pdf
2004
Cited alongside, same era.
Johnson, O. Information theory and the central limit theorem. Imperial College Press, London, 2004. xiv+209 pp
2004
Cited alongside, same era.
Johnson, O.; Barron, A. Fisher information inequalities and the central limit theorem. Probab. Theory Related Fields 129 (2004), no. 3, 391–409
2004
Cited alongside, same era.
Bishop, C. M. Pattern recognition and machine learning. Information Science and Statistics. Springer, New York, 2006. xx+738 pp
2006
Bobkov, S. G.; Chistyakov, G. P.; Götze, F. Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem. Ann. Probab. 41 (2013), no. 4, 2479–2512
2013
Later among the works it cites.
Caglar, U.; Werner, E. Divergence for s-concave and log concave functions. Adv. Math. 257 (2014), 219–247
2014
Later among the works it cites.
van Erven, T.; Harremoës, P. Rényi divergence and Kullback-Leibler divergence. IEEE Trans. Inform. Theory 60 (2014), no. 7, 3797–3820
2014
Later among the works it cites.
Wang, L.; Madiman, M. Beyond the entropy power inequality, via rearrangements. IEEE Trans. Inform. Theory (2014), vol. 60, no. 9, 5116–5137
2014
Later among the works it cites.
Caglar, U.; Fradelizi, M.; Guédon, O.; Lehec, J.; Schütt C.; Werner, E. Functional versions of L p L^{p} -affine surface area and entropy inequalities. Int. Math. Res. Not. IMRN 2016, no. 4, 1223–1250
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Cover, T. M.; Thomas, J. A. Elements of Information Theory. Second edition. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006, xxiv+748 pp
2006
Cited alongside, same era.
Bobkov, S. G.; Madiman, M. The entropy per coordinate of a random vector is highly constrained under convexity conditions. IEEE Trans. Inform. Theory 57 (2011), no. 8, 4940–4954
2011
Cited alongside, same era.
Bobkov, S. G.; Madiman, M. Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures. J. Funct. Anal. 262 (2012), no. 7, 3309–3339
2012
Cited alongside, same era.
Bobkov, S. G. Entropic approach to E. Rio’s central limit theorem for W 2 W_{2} transport distance. Statist. Probab. Lett. 83 (2013), no. 7, 1644–1648
2013
Cited alongside, same era.
Cited in the paper.
Cited in the paper.
Cited in the paper.
2016
Later among the works it cites.
Chung, H. W.; Sadler, B. M.; Hero A. O. Bounds on variance for unimodal distributions. IEEE Trans. Inform. Theory 63 (2017), no. 11, 6936–6949
2017
Later among the works it cites.
Madiman, M.; Melbourne, J.; Xu, P. Forward and reverse entropy power inequalities in convex geometry. Convexity and concentration, 427–485, IMA Vol. Math. Appl., 161, Springer, New York, 2017
2017
Later among the works it cites.
Marsiglietti, A.; Kostina, V. A lower bound on the differential entropy of log-concave random vectors with applications. Entropy 20 (2018), no. 3, 24 pp
2018
Later among the works it cites.
Melbourne, J; Madiman, M.; Salapaka, M. V. Relationships between certain f-divergences. In 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1068–1073
2019
Closest in time.