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Quantum entropy and central limit theorem. [PDF]
Proc Natl Acad Sci U S A, 2023 Significance Convolution has a significant impact on many scientific disciplines, ranging from probability theory and harmonic analysis to information theory.
Bu K, Gu W, Jaffe A.
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Central limit theorem: the cornerstone of modern statistics. [PDF]
Korean J Anesthesiol, 2017 According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, σ2n.
Kwak SG, Kim JH.
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Asymptotic constants for minimal distance in the central limit theorem
Electronic Communications in Probability, 2011 In this paper, we generalize the asymptotic result of Esseen (1958) concerning the Wasserstein distance of order one in the mean central limit theorem to the Wasserstein distances of order $r$ for $r \in ]1,2]$.
Emmanuel Rio
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Mesoscopic central limit theorem for the circular $\beta $-ensembles and applications
Electronic Journal of Probability, 2021 We give a simple proof of a central limit theorem for linear statistics of the circular $\beta $-ensembles which is valid at almost microscopic scales for functions of class $C^{3}$.
Gaultier Lambert
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CONDITIONED LIMIT THEOREMS [PDF]
The Annals of Mathematical Statistics, 1963 Abstract : Limit theorems for Markoff processes and suitable functionals defined on the processes occur in two principal contexts. The first context treats a situation where the limit process is one of the classical stable processes. The usual approximating processes are sums of independent random variables.
Dwass, Meyer, Karlin, Samuel
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Mean field analysis of neural networks: A central limit theorem [PDF]
Stochastic Processes and their Applications, 2018 We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of stochastic ...
Justin A. Sirignano, K. Spiliopoulos
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From the master equation to mean field game limit theory: a central limit theorem [PDF]
Electronic Journal of Probability, 2018 Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential games with $n$ players interacting with one another through their common empirical distribution.
F. Delarue, D. Lacker, K. Ramanan
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A central limit theorem for the stochastic heat equation [PDF]
Stochastic Processes and their Applications, 2018 We consider the one-dimensional stochastic heat equation driven by a multiplicative space-time white noise. We show that the spatial integral of the solution from $-R$ to $R$ converges in total variance distance to a standard normal distribution as $R ...
Jingyu Huang, D. Nualart, L. Viitasaari
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On Shige Peng’s central limit theorem [PDF]
Stochastic Processes and their Applications, 2018 We give error estimates in Peng's central limit theorem for not necessarily nondegenerate case. The exposition uses the language of the classical probability theory instead of the language of the theory of sublinear expectations. We only consider the one-
N. Krylov
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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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