Geodesic
Conditional limit theorem for products of random matrices
Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 371-389

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Products of independent random matrices with identical densities with respect to the Haar measure on the group of unimodular matrices $\operatorname{SL}(m,\mathbb R)$ are considered. With the standard normalization, the conditional distributions of such products, given that these products belong to some compactum, are shown to converge weakly to the distributions of the Brownian bridge. 
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     author = {A. V. Letchikov},
     title = {Conditional limit theorem for products of random matrices},
     journal = {Sbornik. Mathematics},
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     volume = {186},
     number = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_3_a4/}
}
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A. V. Letchikov. Conditional limit theorem for products of random matrices. Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 371-389. http://geodesic.mathdoc.fr/item/SM_1995_186_3_a4/