La démonstration du second théorème limite du calcul de probabilité par la méthode de Cauchy-Lévy reposant sur la fonction caractéristique
Laplace transform estimates and deviation inequalities
Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences
To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite Markov...
Large deviations, central limit theorems and convergence for Young measures and stochastic homogenizations
Large deviations, central limit theorems and Lp convergence for Young measures and stochastic homogenizations
We study the stochastic homogenization processes considered by Baldi (1988) and by Facchinetti and Russo (1983). We precise the speed of convergence towards the homogenized state by proving the following results: (i) a large deviations principle holds for the Young measures; if the Young measures are evaluated on a given function, then (ii) the speed of convergence is bounded in every Lp norm by an explicit rate and (iii) central limit theorems hold. In dimension 1, we apply these results...
Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices
Large scale behavior of semiflexible heteropolymers
We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative...
Lattice paths, sampling without replacement, and limiting distributions.
Lattice point problems and the central limit theorem in Euclidean spaces.
Laws of large numbers and the central limit theorems on a logic
Le mouvement brownien de Lévy indexé par comme limite centrale de temps locaux d’intersection
Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach (suite et fin)
Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach
Level crossings and other level functionals of stationary Gaussian processes.
Likelihood and parametric heteroscedasticity in normal connected linear models
A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.
Limit distributions for sums of shrunken random variables [Book]
Limit laws for a coagulation model of interacting random particles
Limit laws for the energy of a charged polymer
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j<k≤nωjωk1{Sj=Sk} of the polymer {S1, …, Sn} equipped with random electrical charges {ω1, …, ωn}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j<k≤n1{Sj=Sk} run by the d-dimensional random walk {Sk}. As partially needed for our main objective and partially motivated by their independent interest,...
Limit laws for transient random walks in random environment on
We consider transient random walks in random environment on with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characterization of this stable law. The case of Dirichlet environment turns out to be remarkably explicit.
Limit laws of transient excited random walks on integers
We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, δ, is larger than 1 then ERW is transient to the right and, moreover, for δ>4 under the averaged measure it obeys the Central Limit Theorem. We show that when δ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited random...