A limit theorem for empirical distribution functions
M. Fisz (1958)
Studia Mathematica
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M. Fisz (1958)
Studia Mathematica
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B. Diviš, B. Novák (1974)
Acta Arithmetica
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Andrzej Schinzel (1973)
Acta Arithmetica
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Yehoram Gordon, Marius Junge (1999)
Studia Mathematica
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There exists an absolute constant such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that . The concept of volume ratio with respect to -spaces is used to prove the following distance estimate for : .
H. Fiedler, W. Jurkat, O. Körner (1977)
Acta Arithmetica
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Kerbashev, Tzvetozar (1999)
Serdica Mathematical Journal
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The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.
D. Przeworska-Rolewicz (1969)
Studia Mathematica
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K. Ramanathan (1984)
Acta Arithmetica
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Amine Asselah (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider estimates, that is when we average over both randomness, in dimension three or more. We obtain a large deviation principle, and an explicit rate function for a large class of charge distributions.