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))}.
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 .
László Erdős, Benjamin Schlein, Horng-Tzer Yau, Jun Yin (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues { }=1 are close to their classical location { }=1 determined by the...
Christophe Gallesco (2013)
ESAIM: Probability and Statistics
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We consider, in the continuous time version, independent random walks on Z in random environment in Sinai’s regime. Let be the first meeting time of one pair of the random walks starting at different positions. We first show that the tail of the quenched distribution of , after a suitable rescaling, converges in probability, to some functional of the Brownian motion. Then we compute the law of this functional. Eventually, we obtain results about the...
Jean-Paul Ibrahim (2011)
ESAIM: Probability and Statistics
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Following the recent investigations of Baik and Suidan in [(2005) 325–337] and Bodineau and Martin in [10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, (2005) 325–337] and [T. Bodineau and J. Martin, 10 (2005) 105–112 (electronic)],...
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
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...
Antoine Chambaz (2010)
ESAIM: Probability and Statistics
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This paper is devoted to the study of some asymptotic properties of a -estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes recovery of sets. It involves various techniques, including -estimation method, concentration inequalities, maximal inequalities for dependent random variables and -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply...