Showing papers on "Gaussian measure published in 1992"

Polynomial averages in the Kontsevich model

Abstract: We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic potential) measure, as derivatives of the partition function with respect to traces of inverse odd powers of the external argument. The proofs are based on elementary algebraic identities involving a new set of invariant polynomials of the linear group, closely related to the general Schur functions.

Cotype and (q, 1)-summing norm in a Banach space

Abstract: We use modern probabilistic methods to gain a better understanding of what it means that a Banach space fails to be of cotypeq,q>2. In particular, we prove that a Banach space is of cotypeq if and only if the identity map is (q, 1)-summing. (In a previous work, we had shown that this fails forq=2.)

Speech recognition in noise using a projection-based likelihood measure for mixture density HMM's

Abstract: In this study, a cepstral likelihood measure based on the projection operation is incorporated into a mixture density hidden Markov model (HMM) scheme to improve recognition in the presence of additive noise. The case in which the models are determined only under noise-free conditions is addressed. A background discussion and a derivation of the measure are provided. Recognition experiments are presented showing the usefulness of the proposed measure over the standard Gaussian measure (weighted Euclidean distance) for speaker independent, isolated word recognition in noise. It was found that the proposed mixture weighted projection measure significantly improved performance in several noise types, including white, jittering white, and colored noise. As an example, at an SNR of 10-dB white noise, recognition improved from only 38.4% correct using the Gaussian measure to 83.6% using the developed measure. >

Stable measure of a small ball

Abstract: Let p. be a symmetric p-stable measure on a Banach space (E, || • ||) . We prove that /?{||x|| < t) < Kt, where the constant K is independent of all properties of p except for the measure of the unit ball /?{||x|| < 1} .

Operator-decomposability of Gaussian measures on separable Banach spaces

Abstract: An operator-decomposable Gaussian measure on a separable Banach space can be factorized into a convolution product of a strongly operator-decomposable Gaussian measure and an operator-invariant Gaussian measure (with respect to the same operator). An example for this very factorization is discussed in some detail. In particular it is shown that a strongly operator-decomposable Gaussian measure need not necessarily be supported by the contraction subspace of the operator involved. Finally, the decomposability semigroup of a Gaussian measure turns out to be convex; and the corresponding invariance semigroup belongs to its extreme boundary.

Comparison of location models for stochastic processes

Abstract: Let $$\mathfrak{E}$$ (Q) be the statistical experiment based on the observation of an unknown function in the presence of an additive noise process with distributionQ. The (possible) loss of information whenQ is replaced by some other noise distributionP is measured by the deficiency of $$\mathfrak{E}$$ (P) relative to $$\mathfrak{E}$$ (Q). This deficiency and its relation to the variational distance ofP andQ are studied mainly for Gaussian noise processes. Gaussian diffusion processes and special set-indexed processes are treated in detail.

On Large Deviations of Gaussian Measures in Banach Spaces

Abstract: Throughout this paper E will denote a separable Banach space and γ will be a full centered Gaussian measure on E. Define an operator S: E’ → E by S f = ∫ x f(x)γ(dx), and a scalar product γ on SE’ by $$ _\gamma =\int f(x)g(x)\gamma(dx) $$ The completion of S E’ with respect to the norm ∥x;∥γ = √ γ is denoted by Hγ and called the reproducing kernel Hilbert space of γ. Since $$||Sf||\leq _{||g||E^{*}\leq1}^ p [\int g^{2}(x)\gamma(dx)]^{1/2}\cdot ||Sf||_{\gamma} $$ Hγ can and will be viewed as a subset of E. For details on the construction and properties of the reproducing kernel Hilbert space we refer the reader to [2] or [5].

Measurable linear functionals and operators on Fréchet spaces

Abstract: The structure of measurable linear functionals and operators on Frechet spaces with so-called stochastic bases is described.

Linear transformations of Wiener integrals

Abstract: In this paper we obtain a linear transformation theorem in which the Radon-Nikodym derivative is very closely related to the transformation. We also obtain a vector-valued conditional version of this linear transformation theorem

Ferromagneticity of simplicial fields on two‐dimensional compact manifolds

Abstract: Smooth triangulations of a compact smooth connected two‐dimensional Riemannian manifold M are considered The q‐simplicial fields are defined with values in the space of q‐cochains and a natural Gaussian measure is defined giving their distribution, with covariance defined essentially in terms of the combinatorial Laplacian Δc In the continuum limit this measure for q=0 is the free quantum field measure over M In this case it is shown that for a certain collection of triangulations there exists a sequence of subdivisions of each triangulation such that the corresponding measure is ferromagnetic It is also shown that for sufficiently fine subdivisions −Δ+m2I, m≳0 has nonpositive off‐diagonal elements The proofs are obtained by a result on triangulations by simplexes with acute angles It is also proven that the probability measures describing quantum fields on M with polynomial, trigonometric, or exponential interactions satisfy FKG inequalities

Random surface geometries with applications to image processing

Abstract: A procedure is introduced for incorporating into image processing methods a priori 3-dimensional geometrical information about shapes of objects of interest. The information is built in by way of probability measures on deformations of a polyhedral “template.” In order to understand the regularity of the resulting deformations, one needs a theory about the continuum which consists of probability measures on analogous deformations of a smooth compact 2-dimensional manifold template. The theory is constructed via Gaussian measures on an enlargement of the space of triplets of exact one-forms of M, such that with probability 1 the deformations are continous (and have additional regularity). The triplets can be viewed as a “generalized differential map.”