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We develop a scheme to exactly evaluate the correlation energy in the random-phase approximation, based on linear response theory. It is demonstrated that our formula is completely equivalent to a contour integral representation recently…

We determine the critical equation of state of three-dimensional randomly dilute Ising systems, i.e. of the random-exchange Ising universality class. We first consider the small-magnetization expansion of the Helmholtz free energy in the…

We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…

The present study regards the zeroth order mean field approximation of a dipole-type interaction model, which is analytically solved in the canonical and microcanonical ensembles. After writing the canonical partition function, the free and…

An exact solution to the problem of parametric level statistics in non-Gaussian ensembles of N by N Hermitian random matrices with either soft or strong level confinement is formulated within the framework of the orthogonal polynomial…

We consider the free energy of the bipartite spherical Sherrington--Kirkpatrick model. We find the critical temperature and prove the limiting free energy for all non-critical temperature. We also show that the law of the fluctuation of the…

We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…

A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming…

Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has…

We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the problem in a compact set with the topology both of the interval…

To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for…

Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of…

Recently, an exact Green's function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was derived. Here, we use the obtained Green's function to calculate…

We calculate the free energy of the disordered urn model using the law of large numbers. It is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method.…

We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy…

We consider pairing in a dilute system of Fermions with a short-range interaction. While the theory is ill-defined for a contact interaction, the BCS equations can be solved in the leading order of low-energy effective field theory. The…

The ground state solution of the random dimer model is at a critical point after, which has been shown with random link excitations. In this paper we test the robustness of the random dimer model to the random link excitation by imposing…

We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…

We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…

We establish a procedure to find the extremal density matrices for any finite Hamiltonian of a qudit system. These extremal density matrices provide an approximate description of the energy spectra of the Hamiltonian. In the case of…