Quantum fluctuations of a certain class of bulk operators defined in spatial subvolumes of Minkowski space-time, have an unexpected area scaling property. We wish to present evidence that such area scaling may be ascribed to a boundary theory. We first highlight the implications of area scaling with two examples in which the boundary area of the spatial regions is not monotonous with their volu...

A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoil...

Recently, Grosse and Lechner introduced a novel deformation procedure for non–interacting quantum field theories, giving rise to interesting examples of wedge–localized quantum fields with a non–trivial scattering matrix. In the present article we outline an extension of this procedure to the general framework of quantum field theory by introducing the concept of warped convolutions: given a th...

Color quantization of still images can be easily stated as a clustering problem. Color quantization of sequences of images becomes a non-stationary clustering problem. In this paper we propose a very simple and effective evolutive strategy to perform adaptively the computation of the color representatives for each image in the sequence. Salient features of the evolutive strategy proposed here a...

For a Gaussian measure on a separable Hilbert space with covariance operator C, we show that the family of conditional measures associated with conditioning on a closed subspace S are Gaussian with covariance operator the short S(C) of the operator C to S. We provide two proofs. The first uses the theory of Gaussian Hilbert spaces and a characterization of the shorted operator by Andersen and T...

Introduction Conclusions References

This paper addresses the direct and inverse source problems for stochastic acoustic, biharmonic, electromagnetic, elastic wave equations in a unified framework. The driven is assumed to be centered generalized microlocally isotropic Gaussian random field, whose covariance relation operators are classical pseudodifferential operators. Given source, shown well-posed sense of distributions regular...

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.