Publication

Scaling limits for fractional polyharmonic Gaussian fields

2026

Abstract

This work is concerned with fractional Gaussian fields, i.e., Gaussian fields whose covariance operator is given by the inverse fractional Laplacian (−Δ)−s (where, in particular, we include the case s>1). We define a lattice discretization of these fields and show that their scaling limits, with respect to the optimal Besov space topology (up to an endpoint case), are the original continuous fields. As a byproduct, in dimension d1). Nous définissons une discrétisation en réseau de ces champs et montrons que leurs limites d’échelle, par rapport à la topologie optimale de l’espace de Besov (à l’exception d’un cas limite), sont les champs continus originaux. En conséquence, dans les dimensions d

Official source

https://infoscience.epfl.ch/entities/publication/88d4329d-52d6-4c4c-8546-0d031da29e6d

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/88d4329d-52d6-4c4c-8546-0d031da29e6d

About this result

Related concepts (32)

Gaussian process

In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g.

Covariance matrix

In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions.

Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as or Gaussian integers share many properties with integers: they form a Euclidean domain, and have thus a Euclidean division and a Euclidean algorithm; this implies unique factorization and many related properties. However, Gaussian integers do not have a total ordering that respects arithmetic.

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Scaling limits for fractional polyharmonic Gaussian fields

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