Displaying similar documents to “A note on quenched moderate deviations for Sinai's random walk in random environment”

Sojourn time in ℤ+ for the Bernoulli random walk on ℤ

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...

Sojourn time in ℤ for the Bernoulli random walk on ℤ

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 p ∈ (0,1) and q = 1 − p. 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...

Meeting time of independent random walks in random environment

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...

Smooth and sharp thresholds for random -XOR-CNF satisfiability

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 .

Large deviations for directed percolation on a thin rectangle

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)],...

Random Generation for Finitely Ambiguous Context-free Languages

Alberto Bertoni, Massimiliano Goldwurm, Massimo Santini (2010)

RAIRO - Theoretical Informatics and Applications

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We prove that a word of length from a finitely ambiguous context-free language can be generated at random under uniform distribution in ( log ) time by a probabilistic random access machine assuming a logarithmic cost criterion. We also show that the same problem can be solved in polynomial time for every language accepted by a polynomial time -NAuxPDA with polynomially bounded ambiguity.

Product of exponentials and spectral radius of random k-circulants

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...

On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case

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 𝔼 [ log A 1 ] = 0 , 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...

A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions

Gregory F. Lawler (2010)

ESAIM: Probability and Statistics

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The growth exponent for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius is of order . We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem.