Related papers: Virial Expansions for Correlation Functions in Can…
The calculation of the density matrix for fermions and bosons in the Grand Canonical Ensemble allows an efficient way for the inclusion of fermionic and bosonic statistics at all temperatures. It is shown that in a Path Integral Formulation…
This paper studies high-dimensional canonical correlation analysis (CCA) with an emphasis on the vectors that define canonical variables. The paper shows that when two dimensions of data grow to infinity jointly and proportionally, the…
We survey the current status of universality limits for $m$-point correlation functions in the bulk and at the edge for unitary ensembles, primarily when the limiting kernels are Airy, Bessel, or Sine kernels. In particular, we consider…
It is quite common for functional data arising from imaging data to assume values in infinite-dimensional manifolds. Uncovering associations between two or more such nonlinear functional data extracted from the same object across medical…
The properties of discrete nonlinear symmetries of integrable equations are investigated. These symmetries are shown to be canonical transformations. On the basis of the considered examples, it is concluded, that the densities of the…
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
Canonical Correlation Analysis (CCA) is a classical tool for finding correlations among the components of two random vectors. In recent years, CCA has been widely applied to the analysis of genomic data, where it is common for researchers…
The thermodynamics and microstructure of confined fluids with small particle number are best described using the canonical ensemble. However, practical calculations can usually only be performed in the grand-canonical ensemble, which can…
Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
In the context of the Beckerian theory of marriage, when men and women match on a single-dimensional index that is the weighted sum of their respective multivariate attributes, many papers in the literature have used linear canonical…
We present a novel multiview canonical correlation analysis model based on a variational approach. This is the first nonlinear model that takes into account the available graph-based geometric constraints while being scalable for processing…
Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions…
We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression…
Universal limits for the eigenvalue correlation functions in the bulk of the spectrum are shown for a class of nondeterminantal random matrices known as the fixed trace ensemble.
Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble…
We evaluate correlation functions of the BCS model for finite number of particles. The integrability of the Hamiltonian relates it with the Gaudin algebra ${\cal G}[sl(2)]$. Therefore, a theorem that Sklyanin proved for the Gaudin model,…
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…