Geodesic
Stability of the characterization of the multivariate normal distribution in the Skitovich–Darmois theorem
Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 5-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical estimate of stability is obtained in a multidimensional variant of the Skitovich–Darmois theorem when the original random vectors, as well as linear combinations of them, are assumed to be $\varepsilon$-independent. 
@article{ZNSL_1976_61_a0,
     author = {Yu. R. Gabovich},
     title = {Stability of the characterization of the multivariate normal distribution in the {Skitovich{\textendash}Darmois} theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--16},
     year = {1976},
     volume = {61},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a0/}
}
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Yu. R. Gabovich. Stability of the characterization of the multivariate normal distribution in the Skitovich–Darmois theorem. Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 5-16. http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a0/