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We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Mat\'ern fields, are defined via a fractional stochastic differential equation on the compact metric…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
Convex regularization techniques are now widespread tools for solving inverse problems in a variety of different frameworks. In some cases, the functions to be reconstructed are naturally viewed as realizations from random processes; an…
In this paper we study the global fluctuations of block Gaussian matrices within the framework of second-order free probability theory. In order to compute the second-order Cauchy transform of these matrices, we introduce a matricial…
In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…
We generalise the Gaussian formalism of Continuous Variable (CV) systems to describe their interactions with qubits/qudits that result in quantum superpositions of Gaussian processes. To this end, we derive a new set of equations in closed…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin-line bundles of the 2-sphere. In particular,…
For partially coherent light fields with random fluctuations, the intensity distributions and statistics have been proven to be more propagation robust compared with coherent light. However, its full potential in practical applications has…
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study the semi-algebraic geometry of these models, in particular…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
We investigate the statistics of stationary points in the sum of squares of $N$ Gaussian random fields, which we call a "chi-squared" field. The behavior of such a field at a point is investigated, with particular attention paid to the…
We investigate how the consistency relations of large-scale structures are modified when the initial density field is not Gaussian. We consider both scenarios where the primordial density field can be written as a nonlinear functional of a…
We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their…
This paper describes the generation of initial conditions for numerical simulations in cosmology with multiple levels of resolution, or multiscale simulations. We present the theory of adaptive mesh refinement of Gaussian random fields…
This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian…
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and…
Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration…
We introduce a new approach to the spectral equivalence of Gaussian processes and fields, based on the methods of operator theory in Hilbert space. Besides several new results including identities in law of quadratic norms for integrated…