相关论文: A Central Limit Theorem and Exponential Correlatio…

In this article, addressing large $n$ systems, we report that in numerous systems hosting long and short range interactions, multiple correlation lengths may appear. The largest correlation lengths often monotonically increase with…

A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…

We investigate the decay of spatial correlations of $\mathcal{PT}$-symmetric non-Hermitian one-dimensional models that host higher-order exceptional points. Beyond a certain correlation length, they develop anomalous power-law behavior that…

We study a class of interacting particle systems in which $n$ signed particles move on the real line. At close range particles with the same sign repel and particles with opposite sign attract each other. The repulsion and attraction are…

This work presents numerical evidences that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance…

We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a…

We analyze the dynamics of a single-level quantum dot with Coulomb interaction, weakly tunnel coupled to an electronic reservoir, after it has been brought out of equilibrium, e.g. by a step-pulse potential. We investigate the exponential…

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower…

We consider a system of particles lined up on a finite interval with Coulomb 3-dimensional interactions between close neighbours, i.e. only a few other neighbours apart. This model was introduced by Malyshev (2015) to study the flow of…

We use very large cosmological N--body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM)…

Distance correlation coefficient (DCC) can be used to identify new associations and correlations between multiple variables. The distance correlation coefficient applies to variables of any dimension, can be used to determine smaller sets…

We introduce a new paradigm for finite and infinite strict-one-dimensional uniform electron gases. In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. In the high-density limit (small-$r_s$, where…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two…

We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{xy}=J(|x-y|)= J/|x-y|^\alpha$, $J>0$, and $\alpha>d$. As an…

We study the correlations (and alignment as a particular case) existent between the fragments originated in a decaying process when the daughter particles interact. The interaction between the particles is modeled using the potential of…

Considering an example of the long-range Kitaev model, we are looking for a correlation length in a model with long range interactions whose correlation functions away from a critical point have power-law tails instead of the usual…

Results on the correlations of low density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system -- Debye-H\"uckel screening --…

We examine the correlations between rings in random network glasses in two dimensions as a function of their separation. Initially, we use the topological separation (measured by the number of intervening rings), but this leads to…