Geodesic
Rates of clustering in Strassen's law for random polygons
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 57-66

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For partial-sum process generated by a sequence of i.i.d. random variables with mean zero and unit variance necessary and sufficient conditions are obtained for clustering to the Strassen ball with given rate. The answer differs for fast (super-Gaussian) and slow rates. Bibl. 16 titles. 
@article{ZNSL_1996_228_a5,
     author = {A. V. Bulinski and M. A. Lifshits},
     title = {Rates of clustering in {Strassen's} law for random polygons},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {57--66},
     publisher = {mathdoc},
     volume = {228},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a5/}
}
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A. V. Bulinski; M. A. Lifshits. Rates of clustering in Strassen's law for random polygons. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 57-66. http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a5/