Geodesic
Gaussian mixtures and normal approximation for V.\,N.~Sudakov's typical distributions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 37-52

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We derive a general upper bound on the distance of the standard normal law to typical distributions in V. N. Sudakov's theorem (in terms of the weighted total variation). 
@article{ZNSL_2017_457_a3,
     author = {S. G. Bobkov and G. P. Chistyakov and F. G\"otze},
     title = {Gaussian mixtures and normal approximation for {V.\,N.~Sudakov's} typical distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--52},
     publisher = {mathdoc},
     volume = {457},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a3/}
}
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S. G. Bobkov; G. P. Chistyakov; F. Götze. Gaussian mixtures and normal approximation for V.\,N.~Sudakov's typical distributions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 37-52. http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a3/