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Let $X,X_1,...,X_n$ be independent identically distributed random variables.
J. E. Littlewood and A. C. Offord, ”On the number of real roots of a random algebraic equation,” Rec. Math. [Mat. Sbornik] N.S
1943
Earlier work this paper cites.
P. Erdös, ”On a lemma of Littlewood and Offord,” Bull. Amer. Math. Soc
1945
Earlier work this paper cites.
B. A. Rogozin, ”On the increase of dispersion of sums of independent random variables,” Teor. Veroyatn. Primen
1961
Earlier work this paper cites.
C.-G. Esséen, ”On the Kolmogorov–Rogozin inequality for the concentration function,” Z. Wahrscheinlichkeitstheorie Verw. Geb
1966
Earlier work this paper cites.
C.-G. Esséen, ”On the concentration function of a sum of independent random variables,” Z. Wahrscheinlichkeitstheorie Verw. Geb
1968
Earlier work this paper cites.
H. Kesten, ”A sharper form of the Doeblin–Levy–Kolmogorov–Rogozin inequality for concentration functions,” Math. Scand
1969
Earlier work this paper cites.
V. V. Petrov, Sums of Independent Random Variables,
1972
Earlier work this paper cites.
W. Hengartner and R. Theodorescu, Concentration Functions,
1973
Earlier work this paper cites.
G. Halász, ”Estimates for the concentration function of combinatorial number theory and probability,” Periodica Mathematica Hungarica
1977
Earlier work this paper cites.
A. L. Miroshnikov and B. A. Rogozin, ”Inequalities for the concentration functions,” Teor. Veroyatn. Primen
1980
Earlier work this paper cites.
T. V. Arak, ”On the convergence rate in Kolmogorov’s uniform limit theorem. I,” Teor. Veroyatn. Primen
1981
Cited alongside, same era.
A. Yu. Zaitsev, ”Use of the concentration function for estimating the uniform distance,” Zap. Nauchn. Semin. LOMI
1982
Cited alongside, same era.
T. V. Arak and A. Yu. Zaitsev, ”Uniform limit theorems for sums of independent random variables,” Proc. Steklov Inst. Math
1988
Cited alongside, same era.
S. V. Nagaev and S. S. Hodzhabagyan, ”On the estimate for the concentration function of sums of independent random variables,” Teor. Veroyatn. Primen
1996
Cited alongside, same era.
F. Götze and A. Yu. Zaitsev, ”Estimates for the rapid decay of concentration functions of n n -fold convolutions,” J. Theoret. Probab
1998
Cited alongside, same era.
M. Rudelson and R. Vershynin, ”The smallest singular value of a random rectangular matrix,” Comm. Pure Appl. Math
2009
Later among the works it cites.
T. Tao and V. Vu, ”Inverse Littlewood–Offord theorems and the condition number of random discrete matrices,” Ann. Math
2009
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T. Tao and V. Vu, ”From the Littlewood–Offord problem to the circular law: universality of the spectral distribution of random matrices,” Bull. Amer. Math. Soc
2009
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H. Nguyen and V. Vu, ”Optimal inverse Littlewood–Offord theorems,” Adv. Math
2011
Later among the works it cites.
A. Yu. Zaitsev, ”On the rate of decay of concentration functions of n n -fold convolutions of probability distributions,” Vestnik St. Petersburg University: Mathematics
2011
Later among the works it cites.
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F. Götze and A. Yu. Zaitsev, ”A multiplicative inequality for concentration functions of n n -fold convolutions,” In: High dimensional probability, II (Seattle, WA, 1999). Progr. Probab., v. 47
2000
Cited alongside, same era.
J. Bretagnolle, ”Sur l’inégalité de concentration de Doeblin–Lévy, Rogozin-Kesten,” In: Parametric and semiparametric models with applications to reliability, survival analysis, and quality of life. Stat. Ind. Technol., Birkhäuser Boston, Boston, MA (2004), pp. 533–551
2004
Cited alongside, same era.
O. Friedland and S. Sodin, ”Bounds on the concentration function in terms of Diophantine approximation,” C. R. Math. Acad. Sci. Paris
2007
Cited alongside, same era.
M. Rudelson and R. Vershynin, ”The Littlewood–Offord problem and invertibility of random matrices,” Adv. Math
2008
Cited alongside, same era.
Yu. S. Eliseeva and A. Yu. Zaitsev, ”Estimates for the concentration functions of weighted sums of independent random variables,” Teor. Veroyatn. Primen
2012
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2012
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Yu. S. Eliseeva, ”Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables,” Zap. Nauchn. Semin. POMI
2013
Closest in time.