Limit laws for Random matrices and free products.
Dan Voiculescu (1991)
Inventiones mathematicae
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Dan Voiculescu (1991)
Inventiones mathematicae
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Paolo M. Soardi (1986)
Mathematische Zeitschrift
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Manfred Wolff (1979)
Monatshefte für Mathematik
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Yuri Kifer (1996)
Mathematische Zeitschrift
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Gilbert Baumslag (1962)
Mathematische Zeitschrift
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Martin Tretkoff (1973)
Mathematische Zeitschrift
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Gilbert Baumslag, Frank Levin (1965)
Mathematische Zeitschrift
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Marcin Przystalski (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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We consider products of a random number of partial sums of independent, identically distributed, positive square-integrable random variables. We show that the distribution of these products is asymptotically lognormal.
S.K. Zaremba, Z.A. Lomnicki (1956/57)
Mathematische Zeitschrift
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R. Kaufman (1970)
Studia Mathematica
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Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)
Electronic Communications in Probability [electronic only]
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Norman Purzitsky (1972)
Mathematische Zeitschrift
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N. Zygouras (2013)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.
G. Trybuś (1974)
Applicationes Mathematicae
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