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We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means we generalize the large deviation result that was obtained in the homogeneous case by Shao [14] on self-normalized statistics. Furthermore, in the homogenous case, we derive the… (More)

- Mikhail Lifshits, Marguerite Zani
- J. Complexity
- 2008

Let X(t), t ∈ [0, 1] d be an additive random field. We investigate the complexity of finite rank approximation X(t, ω) ≈ n k=1 ξ k (ω)ϕ k (t). The results obtained in asymptotic setting d → ∞, as suggested H.Wo´zniakowski, provide quantitative version of dimension curse phenomenon: we show that the number of terms in the series needed to obtain a given… (More)

- D. Bakry, M. Zani
- 2013

We consider Brownian motions and other processes (Ornstein-Uhlenbeck processes, spherical Brownian motions) on various sets of symmetric matrices constructed from algebra structures, and look at their associated spectral measure processes. This leads to the identification of the multiplicity of the eigenvalues, together with the identification of the… (More)

- D. Bakry, M. Zani
- 2013

Generalizing the work of [5, 41], we give a general solution to the following problem: describe the triplets (Ω, g, µ) where g = (g ij (x)) is the (co)metric associated to the symmetric second order differential operator L(f) = 1 ρ ij ∂ i (g ij ρ∂ j f), defined on a domain Ω of R d and such that L is expandable on a basis of orthogonal polynomials on L 2… (More)

- Marguerite Zani
- 2013

In this paper, we show large deviations for random step functions of type Z n (t) = 1 n [nt] k=1 X 2 k , where {X k } k is a stationary Gaussian process. We deal with the associated random measures ν n = 1 n n k=1 X 2 k δ k/n. The proofs require a Szegö theorem for generalized Toeplitz matrices, which is presented in the Appendix and is analogous to a… (More)

- Mikhail Lifshits, Marguerite Zani
- J. Complexity
- 2015

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