Related papers: Virial Expansions for Correlation Functions in Can…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a $N\times N$ random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding an…
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
Application of the density functional formalism to the canonical ensemble is of practical interest in cases where there is a marked difference between, say, the canonical and the grand canonical ensemble (cavities or pores). An important…
We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to canonical correlation analysis. The challenge is to adjust for the selection…
The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalised to discrete settings involving either a linear or exponential lattice. The corresponding correlation functions can be expressed…
We study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at criticality, the constraint can induce new…
A recent description of an exact map for the equilibrium structure and thermodynamics of a quantum system onto a corresponding classical system is summarized. Approximate implementations are constructed by pinning exact limits (ideal gas,…
The correlations in classical multi-component ionic mixtures with spatial dimension $d\geq 2$ are studied by using a restricted grand-canonical ensemble and the associated hierarchy equations for the correlation functions. Sum rules for the…
We calculate the susceptibility of a canonical ensemble of quantum oscillators to the singular random metric. If the covariance of the metric is $\vert {\bf x}-{\bf x}^{\prime}\vert^{-4\alpha}$ $0< \alpha<\frac{1}{2}$ then the expansion of…
We describe in detail the solution of the extension of the chiral Gaussian Unitary Ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we…
We consider a classical system of $N$ particles confined in a box $\Lambda\subset\mathbb{R}^d$ interacting via a finite range pair potential. Given the validity of the cluster expansion in the canonical ensemble we compute the error between…
Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails,…
A derivation of the Fluctuation-Dissipation Theorem for the microcanonical ensemble is presented using linear response theory. The theorem is stated as a relation between the frequency spectra of the symmetric correlation and response…
We propose a description of pairing properties in finite systems within the canonical and microcanonical ensembles. The approach is derived by solving the BCS and self-consistent quasiparticle random-phase approximation with the…
We compute the large scale (macroscopic) correlations in ensembles of normal random matrices with an arbitrary measure and in ensembles of general non-Hermition matrices with a class of non-Gaussian measures. In both cases the eigenvalues…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
Two basic correlation functions are calculated for a model of $N$ harmonically interacting identical particles in a parabolic potential well. The density and the pair correlation function of the model are investigated for the boson case.…