Related papers: Rearrangements of gaussian fields
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
In this paper we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
We describe two classes of Gaussian self-similar random fields: with strictly stationary rectangular increments and with mild stationary rectangular increments. We find explicit spectral and moving average representations for the fields…
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
We construct a dynamical field theory for noninteracting Brownian particles in the presence of a quenched Gaussian random potential. The main variable for the field theory is the density fluctuation which measures the difference between the…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
We derive an asymptotic expansion for the quadratic variation of a stochastic process satisfying a stochastic differential equation driven by a fractional Brownian motion, based on the theory of asymptotic expansion of Skorohod integrals…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
In this note, we provide an adaptation of the Kohler-Jobin rearrangement technique to the setting of the Gauss space. As a result, we prove the Gaussian analogue of the Kohler-Jobin's resolution of a conjecture of P\'{o}lya-Szeg\"o: when…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…