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The survey is dedicated to a celebrated series of quantitave results, developed by the Lithuanian school of probability, on the normal approximation for a real-valued random variable.
Moment estimates of rosenthal type via cumulants, 2019
P. Eichelsbacher and L. Knichel · 1901
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H. Pitters · 1903
Earlier work this paper cites.
The derivation of the pattern formulae of two-way partitions from those of simpler patterns
R. A. Fisher and J. Wishart · 1931
Earlier work this paper cites.
Sur un nouveau théorème-limite de la théorie des probabilités
H. Cramér · 1938
Earlier work this paper cites.
The accuracy of the Gaussian approximation to the sum of independent variates
A. C. Berry · 1941
Earlier work this paper cites.
Values of Mills’ ratio of area to bounding ordinate and of the normal probability integral for large values of the argument
R. D. Gordon · 1941
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Generalization of Cramér’s limit theorem
V. V. Petrov · 1954
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Contribution aux applications statistiques de la théorie de l´information
P. M. Schützenberger · 1954
Earlier work this paper cites.
A remark on Stirling’s formula
H. Robbins · 1955
Earlier work this paper cites.
On a method of semi-invariants
V. P. Leonov and A. N. Širjaev · 1959
Earlier work this paper cites.
On deviations of the sample mean
R. R. Bahadur and R. Ranga Rao · 1960
Earlier work this paper cites.
Limit theorems for sums of independent variables, taking large deviations into account. II
Yu. V. Linnik · 1961
Earlier work this paper cites.
Limit theorems for the sums of independent variables taking into account the large deviations. I
Yu. V. Linnik · 1961
Earlier work this paper cites.
Limit theorems for sums of independent quantities, taking large deviations into account. III
Yu. V. Linnik · 1962
Earlier work this paper cites.
Convergence of virial expansions
J. L. Lebowitz and O. Penrose · 1964
Earlier work this paper cites.
Some limit theorems for large deviations
S. V. Nagaev · 1965
Earlier work this paper cites.
On the closeness of the distributions of two sums of independent random variables
V. M. Zolotarev · 1965
Earlier work this paper cites.
On large deviations
V. A. Statulevičius · 1966
Earlier work this paper cites.
A sharpening of the inequality of Berry-Esseen
V. M. Zolotarev · 1967
Earlier work this paper cites.
Limit distributions for sums of independent random variables
B. V. Gnedenko and A. N. Kolmogorov · 1968
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Statistical mechanics: Rigorous results
D. Ruelle · 1969
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An introduction to probability theory and its applications. Vol. II
W. Feller · 1971
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Independent and stationary sequences of random variables
I. A. Ibragimov and Yu. V. Linnik · 1971
Earlier work this paper cites.
Decrease properties of truncated correlation functions and analyticity properties for classical lattices and continuous systems
M. Duneau, D. Iagolnitzer, and B. Souillard · 1973
Earlier work this paper cites.
Local limit theorems with regard to large deviations when Cramér’s condition is not satisfied
A. V. Nagaev · 1973
Earlier work this paper cites.
Limit theorems that take into account large deviations in the case when Ju. V. Linnik’s condition is satisfied
L. Saulis · 1973
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Statistical inference for stationary point processes
D. R. Brillinger · 1975
Earlier work this paper cites.
Asymptotische Entwicklungen für Wahrscheinlichkeiten grosser Abweichungen
W. Wolf · 1977
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Lee-Yang theory and normal fluctuations
D. Iagolnitzer and B. Souillard · 1979
Earlier work this paper cites.
A general lemma on probabilities of large deviations
R. Rudzkis, L. Saulis, and V. Statuljavičus · 1979
Earlier work this paper cites.
On exponential estimates of the distribution of random variables
R. Bentkus and R. Rudzkis · 1980
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Central limit theorems for point processes
G. Ivanoff · 1982
Earlier work this paper cites.
Cumulants and partition lattices
T. P. Speed · 1983
Earlier work this paper cites.
On moderate deviations of sums of m m -dependent random vectors
L. Heinrich and W.-D. Richter · 1984
Earlier work this paper cites.
Some estimates of the cumulant-generating function of a sum of m m -dependent random vectors and their application to large deviations
L. Heinrich · 1985
Earlier work this paper cites.
Completely analytical interactions: constructive description
R. L. Dobrushin and S. B. Shlosman · 1987
Earlier work this paper cites.
A method for the derivation of limit theorems for sums of weakly dependent random variables: a survey
L. Heinrich · 1987
Earlier work this paper cites.
Tensor methods in statistics
P. McCullagh · 1987
Earlier work this paper cites.
Normal convergence by higher semi-invariants with applications to sums of dependent random variables and random graphs
S. Janson · 1988
Earlier work this paper cites.
Asymptotic techniques for use in statistics
O. E. Barndorff-Nielsen and D. R. Cox · 1989
Earlier work this paper cites.
Limit theorems for large deviations
L. Saulis and V. A. Statulevičius · 1989
Earlier work this paper cites.
Some bounds of cumulants of m m -dependent random fields
L. Heinrich · 1990
Earlier work this paper cites.
A remark on the connection between the large deviation principle and the central limit theorem
W. Bryc · 1993
Cited alongside, same era.
Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
M. A. Arcones · 1994
Cited alongside, same era.
Gaussian fluctuation in random matrices
O. Costin and J. L. Lebowitz · 1995
Cited alongside, same era.
m m -dependent random fields with analytic cumulant generating function
F. Götze, L. Heinrich, and C. Hipp · 1995
Cited alongside, same era.
Limit theorems of probability theory
V. V. Petrov · 1995
Cited alongside, same era.
Modelling extremal events
P. Embrechts, C. Klüppelberg, and T. Mikosch · 1997
Cited alongside, same era.
Mod-discrete expansions
A. D. Barbour, E. Kowalski, and A. Nikeghbali · 2014
Later among the works it cites.
Mod- φ \varphi convergence
F. Delbaen, E. Kowalski, and A. Nikeghbali · 2014
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Relations between cumulants in noncommutative probability
O. Arizmendi, T. Hasebe, F. Lehner, and C. Vargas · 2015
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Moderate deviations for stabilizing functionals in geometric probability
P. Eichelsbacher, M. Raič, and T. Schreiber · 2015
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Mod-Gaussian convergence and its applications for models of statistical mechanics
P.-L. Méliot and A. Nikeghbali · 2015
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Absorption time and tree length of the Kingman coalescent and the Gumbel distribution
M. Möhle and H. Pitters · 2015
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Large deviations techniques and applications
A. Dembo and O. Zeitouni · 1998
Cited alongside, same era.
On convergence rates in the central limit theorems for combinatorial structures
H.-K. Hwang · 1998
Cited alongside, same era.
Large deviations of heavy-tailed sums with applications in insurance
T. Mikosch and A. V. Nagaev · 1998
Cited alongside, same era.
Level spacings distribution for large random matrices: Gaussian fluctuations
A. Soshnikov · 1998
Cited alongside, same era.
On the necessity of the Statulevičius condition in limit theorems for probabilities of large deviations
N. N. Amosova · 1999
Cited alongside, same era.
The early history of the cumulants and the gram-charlier series
A. Hald · 2000
Cited alongside, same era.
Closeness of probability distributions in terms of Fourier-Stieltjes transforms
S. G. Bobkov · 2016
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Mod- ϕ \phi convergence
V. Féray, P.-L. Méliot, and A. Nikeghbali · 2016
Later among the works it cites.
On the strong Brillinger-mixing property of α \alpha -determinantal point processes and some applications
L. Heinrich · 2016
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Central limit theorems, Lee-Yang zeros, and graph-counting polynomials
J. L. Lebowitz, B. Pittel, D. Ruelle, and E. R. Speer · 2016
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Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem
M. Schulte and Ch. Thäle · 2016
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Semialgebraic statistics and latent tree models
P. Zwiernik · 2016
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The circular unitary ensemble and the Riemann zeta function: the microscopic landscape and a new approach to ratios
R. Chhaibi, J. Najnudel, and A. Nikeghbali · 2017
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Statistical mechanics of lattice systems: a concrete mathematical introduction
S. Friedli and Y. Velenik · 2017
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Edgeworth expansions for profiles of lattice branching random walks
R. Grübel and Z. Kabluchko · 2017
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A central limit theorem for vincular permutation patterns
L. Hofer · 2017
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Convex hulls of random walks: expected number of faces and face probabilities
Z. Kabluchko, V. Vysotsky, and D. Zaporozhets · 2017
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Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory
G. Pan, S. Wang, and W. Zhou · 2017
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On the number of segregating sites, 2017
H. Pitters · 2017
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General theorems on large deviations for random vectors
R. Rudzkis and A. Bakshaev · 2017
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H. Cramér and H. Touchette (translator) · 2018
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Weighted dependency graphs
V. Féray · 2018
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Concentration and moderate deviations for Poisson polytopes and polyhedra
J. Grote and Ch. Thäle · 2018
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Gaussian polytopes: a cumulant-based approach
J. Grote and Ch. Thäle · 2018
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Limit theorems for biorthogonal ensembles and related combinatorial identities
G. Lambert · 2018
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Mesoscopic fluctuations for unitary invariant ensembles
G. Lambert · 2018
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Summability of connected correlation functions of coupled lattice fields
J. Lukkarinen, M. Marcozzi, and A. Nota · 2018
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Limit theory for geometric statistics of point processes having fast decay of correlations
B. Błaszczyszyn, D. Yogeshwaran, and J. E. Yukich · 2019
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Determinants of block Hankel matrices for random matrix-valued measures
H. Dette and D. Tomecki · 2019
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Weighted dependency graphs and the Ising model
J. Dousse and V. Féray · 2019
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Singularity analysis for heavy-tailed random variables
N. M. Ercolani, S. Jansen, and D. Ueltschi · 2019
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Mod- ϕ \phi convergence, II: Estimates on the speed of convergence
V. Féray, P.-L. Méliot, and A. Nikeghbali · 2019
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Limit theorems for random simplices in high dimensions
J. Grote, Z. Kabluchko, and Ch. Thäle · 2019
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Central limit theorems and the geometry of polynomials
M. Michelen and J. Sahasrabudhe · 2019
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Central limit theorems from the roots of probability generating functions
M. Michelen and J. Sahasrabudhe · 2019
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Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations
T. Bodineau, I. Gallagher, L. Saint-Raymond, and S. Simonella · 2020
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Precise deviations for disk counting statistics of invariant determinantal processes, 2020
M. Fenzl and G. Lambert · 2020
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Central limit theorems for patterns in multiset permutations and set partitions
V. Féray · 2020
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Graphons, permutons and the thoma simplex: three mod-gaussian moduli spaces
V. Féray, P.-L. Méliot, and A. Nikeghbali · 2020
Later among the works it cites.
Fine asymptotics for models with Gamma type moments
P. Eichelsbacher and L. Knichel · 2021
Closest in time.
The volume of simplices in high-dimensional poisson–delaunay tessellations
A. Gusakova and Ch. Thäle · 2021
Closest in time.
Necessity of the Cramér, Linnik and Statulevičius conditions for the probabilities of large deviations
N. N. Amosova · 2036
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