Francis Comets, Serguei Popov (2010)
ESAIM: Probability and Statistics
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We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is exp{-Const ⋅ ln(1))}.
Aimé Lachal (2012)
ESAIM: Probability and Statistics
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Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters
Aimé Lachal (2012)
ESAIM: Probability and Statistics
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Let (S) be the classical Bernoulli random walk on the integer line with jump parameters ∈ (01) and = 1 − . The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [35 (1949) 605–608], simpler representations may be obtained for its probability...
Bosetto, Elena (1999)
Beiträge zur Algebra und Geometrie
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Le Van Thanh (2006)
ESAIM: Probability and Statistics
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For a sequence of blockwise -dependent random variables {≥ 1}, conditions are provided under which almost surely where {≥ 1} is a sequence of positive constants. The results are new even when . As special case, the Brunk-Chung strong law of large numbers is obtained for sequences of independent random variables. The current work also extends results of Móricz [ (1987) 709–715], and Gaposhkin [. (1994) 804–812]. The sharpness of the results is illustrated by examples. ...
Saralees Nadarajah (2007)
Applicationes Mathematicae
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The gamma and Rayleigh distributions are two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient X/Y is derived when X and Y are independent gamma and Rayleigh random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.
J. Buzzi, L. Zambotti (2012)
Annales de l'I.H.P. Probabilités et statistiques
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G. Edelman, O. Sporns and G. Tononi have introduced the of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural properties, namely invariance under permutations and additivity, and we call any functional satisfying these two properties an . We classify all intricacies in terms of probability laws on the unit interval and study the growth rate of maximal intricacies when the...
Nadia Creignou, Hervé Daudé (2010)
RAIRO - Theoretical Informatics and Applications
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The aim of this paper is to study the threshold behavior for the satisfiability property of a random -XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with variables per equation. For we show the existence of a sharp threshold for the satisfiability of a random -XOR-CNF formula, whereas there are smooth thresholds for and .
Rudolf Grübel, Anke Reimers (2010)
RAIRO - Theoretical Informatics and Applications
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We investigate the number of iterations needed by an addition algorithm due to Burks if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon. ...