A common approach to the many-electron problem (atoms, molecules and solids) is its transformation into a fewer-particle problem. In Density Functional Theory 2 (DFT) one rewrites the ground-state energy of a many-electron system as a functional of just the one-electron density n(r), the diagonal part of the oneparticle reduced density matrix. In recent years, much attention has been devoted to...

In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite approximations. Under suitable growth (resp. convexity) assumptions, obtain uniform-in-time concentration estimates, over infinite) time horizon, for Wasserstein distance between empirical measure its limit, extending work of Bolley–Guillin–Villani (2007).

‎The goal of this study is to introduce an Asymmetric Uniform-Laplace (AUL) distribution‎. ‎We present a detailed theoretical description of this distribution‎. ‎We try to estimate the parameters of AUL distribution using the maximum likelihood method‎. ‎Since the likelihood approach results in complicated forms‎, ‎we suggest a bootstrap-based approach for es...