Fluctuations de la loi empirique de grandes matrices aléatoires
Fluctuations des temps d'occupation d'un site dans l'exclusion simple symétrique
Fluctuations of the empirical entropies of a chain of infinite order.
Fluctuations of the quenched mean of a planar random walk in an i.i.d. Random environment with forbidden direction.
Fractional multiplicative processes
Statistically self-similar measures on [0, 1] are limit of multiplicative cascades of random weights distributed on the b-adic subintervals of [0, 1]. These weights are i.i.d., positive, and of expectation 1/b. We extend these cascades naturally by allowing the random weights to take negative values. This yields martingales taking values in the space of continuous functions on [0, 1]. Specifically, we consider for each H∈(0, 1) the martingale (Bn)n≥1 obtained when the weights take the values −b−H...
Fractions continues multidimensionnelles et lois stables
Functional central limit theorems for seeds in a linear birth and growth model
A problem of heredity of mixing properties (α-mixing, β-mixing and ρ-mixing) from a stationary point process on ℝ × ℝ₊ to a sequence of some of its points called 'seeds' is considered. Next, using the mixing properties, several versions of functional central limit theorems for the distances between seeds and the process of the number of seeds are obtained.
Functional CLT for random walk among bounded random conductances.
Functionals of spatial point processes having a density with respect to the Poisson process
-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Itô chaos expansion. In the second half we obtain more explicit results for a system of -statistics of some parametric models in stochastic geometry. In the logarithmic form functionals are connected to Gibbs models. There is an inequality between moments of Poisson...