Abstract:
Products of independent random matrices with identical densities with respect to the Haar measure on the group of unimodular matrices SL(m,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.
\Bibitem{Let95}
\by A.~V.~Letchikov
\paper Conditional limit theorem for products of random matrices
\jour Sb. Math.
\yr 1995
\vol 186
\issue 3
\pages 371--389
\mathnet{http://mi.mathnet.ru/eng/sm22}
\crossref{https://doi.org/10.1070/SM1995v186n03ABEH000022}
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\zmath{https://zbmath.org/?q=an:0851.60031}
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https://www.mathnet.ru/eng/sm22
https://doi.org/10.1070/SM1995v186n03ABEH000022
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This publication is cited in the following 6 articles:
K. Yu. Zamana, V. Zh. Sakbaev, “Kompozitsii nezavisimykh sluchainykh operatorov i svyazannye s nimi differentsialnye uravneniya”, Preprinty IPM im. M. V. Keldysha, 2022, 049, 23 pp.
R. Sh. Kalmetiev, Yu. N. Orlov, V. Zh. Sakbaev, “Chernoff iterations as an averaging method for random affine transformations”, Comput. Math. Math. Phys., 62:6 (2022), 996–1006
Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman Formulas and the Law of Large Numbers for Random One-Parameter Semigroups”, Proc. Steklov Inst. Math., 306 (2019), 196–211
V. Zh. Sakbaev, “On the law of large numbers for compositions of independent random semigroups”, Russian Math. (Iz. VUZ), 60:10 (2016), 72–76
V. Yu. Protasov, “Asymptotics of Products of Nonnegative Random Matrices”, Funct. Anal. Appl., 47:2 (2013), 138–147
V. Yu. Protasov, “Invariant functions for the Lyapunov exponents of random matrices”, Sb. Math., 202:1 (2011), 101–126
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