Results 231 to 240 of about 240,621 (277)

Quantitative limit theorems for local functionals of arithmetic random waves

, 2016
We consider Gaussian Laplace eigenfunctions on the two-dimensional flat torus (arithmetic random waves), and provide explicit Berry-Esseen bounds in the 1-Wasserstein distance for the normal and non-normal high-energy approximation of the associated ...
G. Peccati, Maurizia Rossi
semanticscholar   +1 more source

Local Limit Theorems for Lattice Random Variables

Theory of Probability & Its Applications, 1992
See the review Zbl 0748.60028.
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A Local Limit Theorem for Moderate Deviations

Bulletin of the London Mathematical Society, 2001
The author establishes a uniform estimate for the mass function \(P(S_m =y)\) of an integer-valued random walk when \(y\to\infty\) and \((y-m\mu)/ \sqrt{m} \to \infty,\) where \(\mu\) is the mean of the step distribution. The assumptions are that the mass function \(p\) of the step distribution is regularly varying at \(\infty\) with \(-\kappa\), where
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Relationship between Local and Integral Limit Theorems

Theory of Probability & Its Applications, 1996
Let \(\{S_n\}\) be the row-sums of a triangular array of row-independent random vectors. The sequence \(\{S_n\}\) obeys an integral limit theorem if \(\sup_{|x|= 1} |Q_n x|\to 0\) and \(Q_n(S_n - A_n)\) converges weakly to an absolutely continuous (AC) distribution with continuous density function \(g(x)\) for some real sequence \(\{A_n\}\) and ...
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Local Limit Theorem

2023
Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, Tianyi Zheng   +4 more
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Local Limit Theorems for Functionals of Random Processes

Theory of Probability & Its Applications, 1989
The author proved the convergence in variation of functionals in random processes by using the method described in his earlier paper, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova, 142, 48-54 (1985; Zbl 0618.60038); English translation in J. Sov. Math. 36, 468-473 (1987).
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On local limit theorems. I

Lithuanian Mathematical Transactions, 1974
Mitalauskas, A., Statulevičius, V.
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Local limit theorems for free groups

Mathematische Annalen, 2001
Let \(G\) be the free group on \(k\geq 2\) generators. For \(g\in G\), let \(|g|\) be its word length and \([g]\in\mathbb{Z}^k\) its image under the Abelianization map \(G\to\mathbb{Z}^k\). Let \(W(n)=\{g\in G:|g|=n\}\) and, for fixed \(\alpha=(\alpha_1,\dots,\alpha_k)\in\mathbb{Z}^k\), let \(W(n,\alpha)=\{g\in W(n):[g]=\alpha\}\).
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The Local Limit Theorem for Cocycles

2016
We prove a Local Limit Theorem with moderate deviations for cocycles over a contracting action.
Yves Benoist, Jean-François Quint
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Local limit theorems. II

Lithuanian Mathematical Journal, 1977
Mitalauskas, A., Statulevičius, V.
openaire   +1 more source