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
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)],...
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 .
Arup Bose, Rajat Subhra Hazra, Koushik Saha (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We consider × random -circulant matrices with → ∞ and = () whose input sequence { }≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + ) moment. We study the asymptotic distribution of the spectral radius, when = + 1. For this, we first derive the tail behaviour of the fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we...
Sara Brofferio, Dariusz Buraczewski, Ewa Damek (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We consider the autoregressive model on ℝ defined by the stochastic recursion = −1 + , where {( , )} are i.i.d. random variables valued in ℝ× ℝ+. The critical case, when , was studied by Babillot, Bougerol and Elie, who proved that there exists a unique invariant Radon measure for the Markov chain { }. In the present paper we prove that the weak limit of properly...
Christoph Baumgarten (2014)
ESAIM: Probability and Statistics
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Given an autoregressive process of order ( = + ··· + + where the random variables , ,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time (survival or persistence probability). Depending on the coefficients ,...,...
Sandrine Péché (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).
Rémi Rhodes, Vincent Vargas (2011)
ESAIM: Probability and Statistics
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We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. 236 (2003) 449–475]. If is a non degenerate multifractal measure with associated metric () = ([]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dim of a measurable set and the Hausdorff dimension dim with respect to of the same set: ζ(dim ()) = dim(). Our results...
Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur (2013)
ESAIM: Probability and Statistics
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This paper deals with the problem of estimating the level sets () = {() ≥ }, with ∈ (0,1), of an unknown distribution function on ℝ . A plug-in approach is followed. That is, given a consistent estimator of , we estimate () by () = { () ≥ }. In our setting, non-compactness property is required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric...