Local Central Limit Theorem for Determinantal Point Processes [PDF]
, 2014 We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel.
Forrester, Peter J., Lebowitz, Joel L.
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A smeary central limit theorem for manifolds with application to high-dimensional spheres [PDF]
, 2018 The (CLT) central limit theorems for generalized Frechet means (data descriptors assuming values in stratified spaces, such as intrinsic means, geodesics, etc.) on manifolds from the literature are only valid if a certain empirical process of Hessians of
B. Eltzner, S. Huckemann
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On mixing and the local central limit theorem for hyperbolic flows [PDF]
Ergodic Theory and Dynamical Systems, 2017 We formulate abstract conditions under which a suspension flow satisfies the local central limit theorem. We check the validity of these conditions for several systems including reward renewal processes, Axiom A flows, as well as the systems admitting ...
D. Dolgopyat, P'eter N'andori
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On Estimation of the Remainder Term in New Asymptotic Expansions in the Central Limit Theorem
Computer Sciences & Mathematics Forum, 2023 We offer a new asymptotic expansion with an explicit remainder estimate in the central limit theorem. The results obtained are essentially based on new forms of asymptotic expansions in the central limit theorem.
Vitaly Sobolev, Sergey Ramodanov
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Central limit theorems for sub-linear expectation under the Lindeberg condition
Journal of Inequalities and Applications, 2018 In this paper, we investigate the central limit theorems for sub-linear expectation for a sequence of independent random variables without assumption of identical distribution. We first give a bound on the distance between the normalized sum distribution
Cheng Hu
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Central limit theorem and Diophantine approximations [PDF]
, 1910 Let $F_n$ denote the distribution function of the normalized sum $Z_n = (X_1 + \dots + X_n)/\sigma\sqrt{n}$ of i.i.d. random variables with finite fourth absolute moment.
Bobkov, Sergey G.
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The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem [PDF]
Advances in Theoretical and Mathematical Physics, 2016 For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-\kappa}$ for some constant $\kappa > 0$. This expansion is
R. Bauerschmidt +3 more
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Central and Local Limit Theorems for Numbers of the Tribonacci Triangle
Mathematics, 2021 In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of ...
Igoris Belovas
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Berry-Esseen theorem and local limit theorem for non uniformly expanding maps [PDF]
, 2004 We prove that, in Young towers with sufficiently small tails, the speed in the central limit theorem is O(1/\sqrt{n}), and the local limit theorem holds.
Gouezel, Sebastien
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Central Limit Theorem for Coloured Hard Dimers
Journal of Probability and Statistics, 2010 We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs.
Maria Simonetta Bernabei, Horst Thaler
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