Invariance Principle for Symmetric Statistics

Sure Invariance Principle for Multivariate Kolmogorov - Smirnov Statistics

An invariance principle for random planar maps

We show a new invariance principle for the radius and other functionals of a class of conditioned ‘Boltzmann-Gibbs’distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in Marckert and Miermont (2006). As in the latter paper, we make use of a bijection between planar maps and a class of labelled multitype trees, due to Bouttier et al. (2...

Strong invariance principle for dependent random fields

A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Csörgő and Révész applied recently by Balan to associated random fields. The key step in our proof combines new moment and maximal inequalities, established by the authors for partial sums of multiindexed random variables, ...

Invariance principle for the Random Conductance Model

We study a continuous time random walk X in an environment of i.i.d. random conductances μe ∈ [0,∞) in Zd. We assume that P(μe > 0) > pc, so that the bonds with strictly positive conductances percolate, but make no other assumptions on the law of the μe. We prove a quenched invariance principle for X, and obtain Green’s functions bounds and an elliptic Harnack inequality.

Hölderian Invariance Principle for Hilbertian Linear Processes

Let (ξn)n≥1 be the polygonal partial sums processes built on the linear processes Xn = ∑ i≥0 ai( n−i), n ≥ 1, where ( i)i∈Z are i.i.d., centered random elements in some separable Hilbert space H and the ai’s are bounded linear operators H → H, with ∑i≥0‖ai‖ < ∞. We investigate functional central limit theorem for ξn in the Hölder spaces H o ρ(H) of functions x : [0, 1] → H such that ‖x(t+ h) − ...