Local limit theorems via Landau-Kolmogorov inequalities

DOI10.3150/13-BEJ590zbMath1320.60065arXiv1011.3100OpenAlexW2054073352MaRDI QIDQ2348728

Nathan Ross, Adrian Roellin

Publication date: 15 June 2015

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.3100

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Random graphs (graph-theoretic aspects) (05C80)

Related Items (19)

KOLMOGOROV BOUNDS FOR THE NORMAL APPROXIMATION OF THE NUMBER OF TRIANGLES IN THE ERDŐS–RÉNYI RANDOM GRAPH ⋮ Local limit theorems and mod-phi convergence ⋮ Multivariate approximation in total variation. II: Discrete normal approximation ⋮ Interval type local limit theorems for lattice type random variables and distributions ⋮ Discretized normal approximation by Stein's method ⋮ Local limit theorems for occupancy models ⋮ Negative dependence and stochastic orderings ⋮ Stein's method for conditional central limit theorem ⋮ When does the chaos in the Curie-Weiss model stop to propagate? ⋮ Classical and almost sure local limit theorems ⋮ Error bounds in local limit theorems using Stein's method ⋮ A local central limit theorem for triangles in a random graph ⋮ Generalized gamma approximation with rates for urns, walks and trees ⋮ Mod-Gaussian Convergence and Its Applications for Models of Statistical Mechanics ⋮ Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs ⋮ Higher-order fluctuations in dense random graph models ⋮ Local central limit theorem for multi-group Curie-Weiss models ⋮ Local central limit theorem for long-range two-body potentials at sufficiently high temperatures ⋮ Convergences of the rescaled Whittaker stochastic differential equations and independent sums

Cites Work

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• Local central limit theorems in stochastic geometry
• Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie-Weiss model
• Stein's method for dependent random variables occuring in statistical mechanics
• Approximation of sums of conditionally independent variables by the translated Poisson distribution
• Zero biasing and a discrete central limit theorem
• Exchangeable pairs and Poisson approximation
• An extension of Mineka's coupling inequality
• When are small subgraphs of a random graph normally distributed?
• A central limit theorem for decomposable random variables with applications to random graphs
• The asymptotic number of labeled graphs with \(n\) vertices, \(q\) edges, and no isolated vertices
• The phase transition in a random hypergraph
• Some inequalities satisfied by the integrals or derivatives of real or analytic functions
• Total variation asymptotics for sums of independent integer random variables
• An elementary proof of the local central limit theorem
• From Stein identities to moderate deviations
• Stein's method for concentration inequalities
• Translated Poisson approximation using exchangeable pair couplings
• A shorter proof of Kanter's Bessel function concentration bound
• The order of the giant component of random hypergraphs
• Limit theorems for sums of dependent random variables occurring in statistical mechanics
• Poisson perturbations
• On Choosing and Bounding Probability Metrics

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