We study the free central limit theorem for not necessarily identically distributed random variables where limiting distribution is semicircle distribution. Starting from an estimate Kolmogorov distance between measure of suitably normalized sums and without any moment condition, we show Lindeberg improve known results on rates convergence under conditions existence third moments.

We study critical points of a Ginzburg-Landau type functional with an attractive-repulsive-attractive nonlocal interaction. Using an appropriate scaling and the Γ-convergence method we reduce the problem to a finite dimensional one. In contrast to a similar problem with just an attractive-repulsive interaction, we obtain a richer set of solutions. The soliton-stripe patterns appear as skewed lo...

We study the asymptotic behaviour of a class of self-attracting motions on R. We prove the decrease of the free energy related to the system and mix it together with stochastic approximation methods. We finally obtain the (limit-quotient) ergodicity of the self-attracting diffusion with a speed of convergence.

We prove that the free energy of any spherical mixed $p$-spin model converges as dimension $N$ tends to infinity. While convergence is a consequence Parisi formula, proof we give independent formula and uses well-known Guerra-Toninelli interpolation method. The latter was invented for models with Ising spins super-additive therefore (normalized by $N$) converges. In case, however, configuration...

In this paper, static and free vibrations behaviors of the orthotropic functionally graded material (FGM) plates resting on the two-parameter elastic foundation are analyzed by the a mesh-free method based on the first order shear deformation plate theory (FSDT). The mesh-free method is based on moving least squares (MLS) shape functions and essential boundary conditions are imposed by transfer...