Related papers: Multivariate Operator-Self-Similar Random Fields
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
Operator regular variation reveals general power-law distribution tail decay phenomena using operator scaling, that includes multivariate regular variation with scalar scaling as a special case. In this paper, we show that a multivariate…
Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to…
The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport processes which are ballistic in a chosen `parallel' direction and diffusive and all other `transverse' directions. The time-space transformations of this Lie…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By…
An operator fractional Brownian field (OFBF) is a Gaussian, stationary increment R^n-valued random field on R^m that satisfies the operator self-similarity property {X(c^E t)}_{t in R^m} L= {c^H X(t)}_{t in R^m}, c > 0, for two matrix…
We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are…
The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance…
Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. The current paper is concerned with the invariance of Modular biframes for operators under some class of…
Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local…
We develop sampling methodology aimed at determining stochastic operators that satisfy a support size restriction on the autocorrelation of the operators stochastic spreading function. The data that we use to reconstruct the operator (or,…
The paper deals with singular Sturm-Liouville expressions with matrix-valued distributional coefficients. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent…
We describe identical particles through their extrinsic physical properties and operationally with an operator of selective measure Mm. The operator Mm is formed through non-symmetrized tensor product of one-particle measurement operators,…
Motivated by recent work of Au, C{\'e}bron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a…
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and…
We consider a class of shift-generated alpha-homogeneous random fields (RFs) C[Z] defined through a functional identity involving a fixed positive alpha and a given jointly measurable R^d-valued RF Z(t),t in R^l. The significance of such…
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymptotic results in terms of random time changes.