相关论文: Rate of Convergence in the entropic free CLT

We prove an expansion for densities in the free CLT and apply this result to an expansion in the entropic free central limit theorem assuming a moment condition of order four for the free summands.

We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of free convolution. We apply these results to the expansion of…

We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.

We provide the first quantitative estimates for the rate of convergence in the free multiplicative central limit theorem (CLT), in terms of the Kolmogorov and $r$-Wasserstein distances for $r \geq 1$. While the free additive CLT has been…

It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that…

In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their…

We establish a central limit theorem (CLT) for families of products of $\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework…

We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy,…

We make use of an entropic property to establish a convergence theorem (Main Theorem), which reveals that the conditional entropy measures the asymptotic Gaussianity. As an application, we establish the {\it entropic conditional central…

We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.

An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.

We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the…

Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given…

This paper is concerned with normal approximation under relaxed moment conditions using Stein's method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of…

We show how the renormalization group approach can be used to prove quantitative central limit theorems (CLTs) in the setting of free, Boolean, bi-free and bi-Boolean independence under finite third moment assumptions. The proofs rely on…

We consider the existence of the integrated density of states (IDS) of the Anderson model on the Hilbert space $\ell^2(\mathbb{Z}^d)$ as analogues to the law of large numbers (LLN). In this work, we prove the analogues central limit theorem…

We study the free central limit theorem for not necessarily identically distributed free random variables where the limiting distribution is the semicircle distribution. Starting from an estimate for the Kolmogorov distance between the…

We prove that the rate of convergence for the central limit theorem in finite free convolution is of order $n^{1/2}$

We obtain concentration estimates for the fluctuations of Coulomb gases in any dimension and in a broad temperature regime, including very small and very large temperature regimes which may depend on the number of points. We obtain a full…

In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this…