Related papers: The Direct-Connectedness Function in the Random Co…
We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…
We calculate, through Monte Carlo numerical simulations, the partial total and direct correlation functions of the three dimensional symmetric Widom-Rowlinson mixture. We find that the differences between the partial direct correlation…
There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent $\langle k^2 \rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf 80}, 1275…
We introduce a non-standard model for percolation on the integer lattice $\mathbb Z^2$. Randomly assign to each vertex $a \in \mathbb Z^2$ a potential, denoted $\phi_a$, chosen independently and uniformly from the interval $[0, 1]$. For…
We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in…
Recently, the classical configuration model for random graphs with given degree distribution has been extensively used as a null model in contraposition to real networks with the same degree distribution. In this paper, we briefly review…
Using recent couplings we provide counterexamples to monotonicity properties of percolation models related to graphical representations of the Ising model. We further prove a new coupling of the double random current model to the…
In this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice $\Z^d$,…
Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and…
We consider generic finite range percolation models on $\mathbb{Z}^d$ under a high temperature assumption (exponential decay of connection probabilities and exponential ratio weak mixing). We prove that the rate of decay of point-to-point…
In the present work we demonstrate the use of a parcellation free connectivity model based on Poisson point processes. This model produces for each subject a continuous bivariate intensity function that represents for every possible pair of…
An important quantity in liquid state theory is the radial distribution function $g(r)$. It can be calculated within the framework of classical density functional theory in two very distinct ways. In the test-particle route, one fixes a…
We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small…
The molecular density functional theory of fluids provides an exact theory for computing solvation free energies in implicit solvents. One of the reasons it has not received nearly as much attention as quantum density functional theory for…
We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching…
We report on recent results that show that the pair correlation function of systems with exponentially decaying interactions can fail to exhibit Ornstein-Zernike asymptotics at all sufficiently high temperatures and all sufficiently small…
We use the lace expansion to prove that the critical values for nearest-neighbour bond percolation on the $n$-cube $\{0,1\}^n$ and on $\mathbb{Z}^n$ have asymptotic expansions, with rational coefficients, to all orders in powers of…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
A general model-independent discussion of mesonic correlation functions is given. We derive new inequalities, including one stronger than Weingarten's inequality. Mesonic correlation functions are calculated in the random instanton vacuum…
A rigorous derivation of the density functional in the Hohenberg-Kohn theory is presented. With no assumption regarding the magnitude of the electric coupling constant $e^2$ (or correlation), this work provides a firm basis for…