Publication

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

Juhan Aru
2022
Journal Articles

Abstract

We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition of the underlying functional space in terms of radial processes and spherical harmonics.

Official source

https://infoscience.epfl.ch/entities/publication/1e808d7c-90a4-41a4-b590-c285d996f0ae

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Juhan Aru
2022
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1e808d7c-90a4-41a4-b590-c285d996f0ae

About this result

Related concepts (16)

Spherical harmonics

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series.

Functional analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous or unitary operators between function spaces.

Functional (mathematics)

In mathematics, a functional (as a noun) is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). In linear algebra, it is synonymous with linear forms, which are linear mappings from a vector space into its field of scalars (that is, they are elements of the dual space ) In functional analysis and related fields, it refers more generally to a mapping from a space into the field of real or complex numbers.

Related publications (22)

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Carl Johan Peter Johansson

. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder

Ursula Röthlisberger, Justin Villard, Martin Peter Bircher

The accurate representation of the structural and dynamical properties of water is essential for simulating the unique behavior of this ubiquitous solvent. Here we assess the current status of describing liquid water using ab initio molecular dynamics, wit ...

Royal Soc Chemistry2024

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Transportation-based functional ANOVA and PCA for covariance operators

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob&apos;s ladder

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Transportation-based functional ANOVA and PCA for covariance operators

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob&apos;s ladder

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder