Optimal Hölderian functional central limit theorems for uniform empirical and quantile

The random graph measure is supposed to be ergodic, to have appropriate moments for the size of finite clusters and, in case it has infinite cluster, to satisfy to a central

Abstract. In this paper, motivated by some applications in branching random walks, we improve and extend his theorems in the sense that: 1) we prove that the central limit theorem

We prove that, in this case, the Open Quantum Random Walk behaves like a mixture of Open Quantum Random Walks with single Gaussian, that is, up to conditioning the trajectories at

Roughly speaking functional central limit theorems hold true as soon as the self-intersection local time of the random walk converges almost surely to some constant.. To be com-

in the (much simpler) case of random fields defined on the circle [19], Section 3, the condi- tions for the central limit theorem could be expressed in terms of convolutions of

The proof is based on a new central limit theorem for dependent sequences with values in smooth Banach spaces, which is given in Section 3.1.1.. In Section 2.2, we state the

We give two main results, which are necessary tools for the study of stability in section 3: we prove uniqueness, up to an additive constant, of the optimal transport

exponential Young funtions for stationary real random elds whih are bounded.. or satisfy some nite exponential