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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
Similarity:
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...
Dennis Komm, Richard Královič (2011)
RAIRO - Theoretical Informatics and Applications
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Recently, a new measurement – the – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, , and the problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our special focus goes to barely random algorithms, ...
Aimé Lachal (2012)
ESAIM: Probability and Statistics
Similarity:
Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters
Dennis Komm, Richard Královič (2011)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Similarity:
Recently, a new measurement – the – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, , and the problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our special focus goes to barely random algorithms, , randomized...
Nadia Creignou, Hervé Daudé (2010)
RAIRO - Theoretical Informatics and Applications
Similarity:
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 .