Related papers: Multivariate Operator-Self-Similar Random Fields
We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of selfsimilar fields. More specifically, we are able to construct any Gaussian field…
Open and Closed super-string field theories are constructed in an event-symmetric target space. The partition functions of Statistical and Quantum models are constructed in terms of invariants defined on Lie-algebra representations. An…
In this work, we investigate the role of multivalued fields in the formulation of monopole operators and their connection with topological states of matter. In quantum field theory it is known that certain states describe collective modes…
The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are…
This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown…
We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a…
Oscillons are long-lived, spatially localized field configurations, which are supported by attractive non-linearities in the scalar potential. We study oscillons comprised of multiple interacting fields, each having an identical potential…
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…
The completely positive maps, a generalization of the nonnegative matrices, are a well-studied class of maps from $n\times n$ matrices to $m\times m$ matrices. The existence of the operator analogues of doubly stochastic scalings of…
Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively…
We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite…
A class of non-linear eigenvalue problems defined in the form of operator polynomials is investigated. The problems are related to wave equations which appear in a relativistic quantum field theory. Spectral asymptotics for this class are…
Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently.…
We consider two natural gradings on the space of symmetric functions: by degree and by length. We introduce a differential operator $T$ that leaves the components of this double grading invariant and exhibit a basis of bihomogeneous…
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…
We explore connections between an operator's matrix element distribution and its entanglement generation. Operators with matrix element distributions similar to those of random matrices generate states of high multi-partite entanglement.…
This article introduces the operator-scaling random ball model, generalizing the isotropic random ball models investigated recently in the literature to anisotropic setup. The model is introduced as a generalized random field and results on…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
Let $\mathbb{R}^N_+= [0,\infty)^N$. We here consider a class of random fields $(X_t)_{t\in \mathbb{R}^N_+}$ which are known as Multiparameter L\'evy processes. Related multiparameter semigroups of operators and their generators are…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…