The Experts below are selected from a list of 89361 Experts worldwide ranked by ideXlab platform
Sigurd Kirkevold Næss - One of the best experts on this subject based on the ideXlab platform.
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Application of the Kolmogorov-Smirnov test to CMB data: Is the universe really weakly random?
Astronomy and Astrophysics, 2012Co-Authors: Sigurd Kirkevold NæssAbstract:A recent application of the Kolmogorov-Smirnov test to the WMAP 7 year W-band maps claims evidence that the CMB is "weakly random", and that only 20% of the signal can be explained as a random Gaussian Field. I here repeat this analysis, and in contrast to the original result find no evidence for deviation from the standard {\Lambda}CDM model. Instead, the results of the original analysis are consistent with not properly taking into account the correlations of the {\Lambda}CDM power spectrum.
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Application of the Kolmogorov-Smirnov test to CMB data: Is the universe really weakly random? (Research Note)
2012Co-Authors: Sigurd Kirkevold NæssAbstract:A recent application of the Kolmogorov-Smirnov test to the WMAP 7 year W-band maps claims evidence that the CMB is “weakly random”, and that only 20% of the signal can be explained as a random Gaussian Field. I here repeat this analysis, and in contrast to the original result find no evidence for deviation from the standard ΛCDM model. Instead, the results of the original analysis are consistent with not properly taking into account the correlations of the ΛCDM power spectrum.
Giovanni Peccati - One of the best experts on this subject based on the ideXlab platform.
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Squared chaotic random variables: new moment inequalities with applications
Journal of Functional Analysis, 2016Co-Authors: Dominique Malicet, Ivan Nourdin, Giovanni Peccati, Guillaume PolyAbstract:We prove a new family of inequalities involving squares of random variables belonging to the Wiener chaos associated with a given Gaussian Field. Our result provides a substantial generalisation, as well as a new analytical proof, of an estimate by Frenkel (2007), and also constitute a natural real counterpart to an inequality established by Arias-de-Reyna (1998) in the framework of complex Gaussian vectors. We further show that our estimates can be used to deduce new lower bounds on homogeneous polynomials, thus partially improving results by Pinasco (2012), as well as to obtain a novel probabilistic representation of the remainder in Hadamard inequality of matrix analysis.
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Strong asymptotic independence on Wiener chaos
2014Co-Authors: Ivan Nourdin, David Nualart, Giovanni PeccatiAbstract:Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian Field. We show that, as $n\to\infty$, the components of $F_n$ are asymptotically independent if and only if ${\rm Cov}(F_{i,n}^2,F_{j,n}^2)\to 0$ for every $i\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-Itô integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosinski.
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Cumulants on the Wiener Space
Journal of Functional Analysis, 2010Co-Authors: Ivan Nourdin, Giovanni PeccatiAbstract:We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian Field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual ``graph/diagram computations'' adopted in most of the probabilistic literature.
Mario Wschebor - One of the best experts on this subject based on the ideXlab platform.
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The Tail of the Maximum of Smooth Gaussian Fields on Fractal Sets
Journal of Theoretical Probability, 2012Co-Authors: Jeanmarc Azais, Mario WscheborAbstract:We study the probability distribution of the maximum MS of a smooth stationary Gaussian Field defined on a fractal subset S of ℝn. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution ℙ(MS>u) as u→+∞. The basic tool is the Rice formula for the moments of the number of local maxima of a random Field.
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The tail of the maximum of smooth Gaussian Fields on fractal sets
arXiv: Probability, 2011Co-Authors: Jeanmarc Azais, Mario WscheborAbstract:We study the probability distribution of the maximum $M_S $ of a smooth stationary Gaussian Field defined on a fractal subset $S$ of $\R^n$. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution $\P(M_S>u)$ as $u\rightarrow +\infty.$ The basic tool is Rice formula for the moments of the number of local maxima of a random Field.
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a general expression for the distribution of the maximum of a Gaussian Field and the approximation of the tail
Stochastic Processes and their Applications, 2008Co-Authors: Jeanmarc Azais, Mario WscheborAbstract:We study the probability distribution F(u) of the maximum of smooth Gaussian Fields defined on compact subsets of having some geometric regularity. Our main result is a general expression for the density of F. Even though this is an implicit formula, one can deduce from it explicit bounds for the density, and hence for the distribution, as well as improved expansions for 1-F(u) for large values of u. The main tool is the Rice formula for the moments of the number of roots of a random system of equations over the reals. This method enables also to study second-order properties of the expected Euler characteristic approximation using only elementary arguments and to extend these kinds of results to some interesting classes of Gaussian Fields. We obtain more precise results for the "direct method" to compute the distribution of the maximum, using the spectral theory of GOE random matrices.
Ivan Nourdin - One of the best experts on this subject based on the ideXlab platform.
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Squared chaotic random variables: new moment inequalities with applications
Journal of Functional Analysis, 2016Co-Authors: Dominique Malicet, Ivan Nourdin, Giovanni Peccati, Guillaume PolyAbstract:We prove a new family of inequalities involving squares of random variables belonging to the Wiener chaos associated with a given Gaussian Field. Our result provides a substantial generalisation, as well as a new analytical proof, of an estimate by Frenkel (2007), and also constitute a natural real counterpart to an inequality established by Arias-de-Reyna (1998) in the framework of complex Gaussian vectors. We further show that our estimates can be used to deduce new lower bounds on homogeneous polynomials, thus partially improving results by Pinasco (2012), as well as to obtain a novel probabilistic representation of the remainder in Hadamard inequality of matrix analysis.
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Strong asymptotic independence on Wiener chaos
2014Co-Authors: Ivan Nourdin, David Nualart, Giovanni PeccatiAbstract:Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian Field. We show that, as $n\to\infty$, the components of $F_n$ are asymptotically independent if and only if ${\rm Cov}(F_{i,n}^2,F_{j,n}^2)\to 0$ for every $i\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-Itô integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosinski.
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Cumulants on the Wiener Space
Journal of Functional Analysis, 2010Co-Authors: Ivan Nourdin, Giovanni PeccatiAbstract:We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian Field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual ``graph/diagram computations'' adopted in most of the probabilistic literature.
Frederi Viens - One of the best experts on this subject based on the ideXlab platform.
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Superdiffusive behavior for a Brownian polymer in a Gaussian medium
Annals of Probability, 2008Co-Authors: Sergio De Carvalho Bezerra, Samy Tindel, Frederi ViensAbstract:This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a space-time Gaussian Field W assumed to be white noise in time and function-valued in space. According to the behavior of the spatial covariance W, we give a lower bound on the power growth (wandering exponent) of the polymer when the time parameter goes to infinity: the polymer is proved to be superdiffusive, with a wandering exponent exceeding any $\alpha
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Superdiffusivity for a Brownian polymer in a continuous Gaussian environment
Annals of Probability, 2008Co-Authors: Sergio Bezerra, Samy Tindel, Frederi ViensAbstract:This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a Gaussian Field W on R+ × R which is white noise in time and functionvalued in space. According to the behavior of the spatial covariance of W, we give a lower bound on the power growth (wandering exponent) of the polymer when the time parameter goes to infinity: the polymer is proved to be superdiffusive, with a wandering exponent exceeding any α