Related papers: Pair correlation densities of inhomogeneous quadra…
We show that polynomial decay of correlations is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of a class of nonuniformly hyperbolic diffeomorphisms for which Young proved polynomial…
We have developed a theory for inhomogeneous systems that allows for incorporation of effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess $\phi({\bf…
We construct real numbers $\alpha$ for which the pair correlation function \[N^{-1}#\{m<n\le N:||\alpha m^2-\alpha n^2||\le XN^{-1}\}\] tends to $X$ as $N$ grows. Moreover we show for any "Diophantine" $\alpha$ that the pair correlation…
We study the $\beta$ analogue of the nonintersecting Poisson random walks. We derive a stochastic differential equation of the Stieltjes transform of the empirical measure process, which can be viewed as a dynamical version of the…
We investigate the value of the correlation function of an inhomogeneous hard-sphere fluid at contact. This quantity plays a critical role in Statistical Associating Fluid Theory (SAFT), which is the basis of a number of recently developed…
We investigate six types of two-point boundary correlation functions in the dense loop model. These are defined as ratios $Z/Z^0$ of partition functions on the $m\times n$ square lattice, with the boundary condition for $Z$ depending on two…
We study a model of a photon mode dipole-coupled to a medium of two-level oscillators in a microcavity in the presence of dephasing processes introduced by coupling to external baths. Decoherence processes can be classified as pair-breaking…
We establish explicit quenched asymptotics for pure-jump symmetric L\'evy processes in general Poissonian potentials, which is closely related to large time asymptotic behavior of solutions to the nonlocal parabolic Anderson problem with…
Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two space-time derivatives of the fields, we…
We study the Sine$_\beta$ process, the bulk point process scaling limit of beta-ensembles. We provide a representation of its pair correlation function for all $\beta>0$ via a stochastic differential equation. We show that the pair…
The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this…
Level density $\rho(E,N,Z)$ is calculated for the two-component close- and open-shell nuclei with a given energy $E$, and neutron $N$ and proton $Z$ numbers, taking into account pairing effects within the microscopic-macroscopic approach…
We prove closed-form identities for the sequence of moments $\int t^{2n}|\Gamma(s)\zeta(s)|^2dt$ on the whole critical line $s=1/2+it$. They are finite sums involving binomial coefficients, Bernoulli numbers, Stirling numbers and $\pi$,…
We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the…
We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance…
We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor…
We discuss particle entanglement in systems of indistinguishable bosons and fermions, in finite Hilbert spaces, with focus on operational measures of quantum correlations. We show how to use von Neumann entropy, Negativity and entanglement…
Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…
We review the properties of chaoticity and coherence in Bose-Einstein condensation and correlations, for a dense boson system in its mean-field represented approximately by a harmonic oscillator potential. The order parameter and the nature…
The two-point correlation function of a Potts model on a graph $G$ may be expressed in terms of the flow polynomials of `Poissonian' random graphs derived from $G$ by replacing each edge by a Poisson-distributed number of copies of itself.…