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A SHARP INVERSE LITTLEWOODOFFORD THEOREM
, 2009
"... Let ηi, i = 1,...,n be iid Bernoulli random variables. Given a multiset v of n numbers v1,..., vn, the concentration probability P1(v) of v is defined as P1(v): = sup x P(v1η1 +...vnηn = x). A classical result of LittlewoodOfford and Erdős from the 1940s asserts that if the vi are nonzero, then t ..."
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Cited by 12 (3 self)
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Let ηi, i = 1,...,n be iid Bernoulli random variables. Given a multiset v of n numbers v1,..., vn, the concentration probability P1(v) of v is defined as P1(v): = sup x P(v1η1 +...vnηn = x). A classical result of LittlewoodOfford and Erdős from the 1940s asserts that if the vi are non
BILINEAR AND QUADRATIC VARIANTS ON THE LITTLEWOODOFFORD PROBLEM
, 2009
"... If f(x1,..., xn) is a polynomial dependent on a large number of independent Bernoulli random variables, what can be said about the maximum concentration of f on any single value? For linear polynomials, this reduces to one version of the classical LittlewoodOfford problem: Given nonzero constants ..."
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Cited by 11 (0 self)
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If f(x1,..., xn) is a polynomial dependent on a large number of independent Bernoulli random variables, what can be said about the maximum concentration of f on any single value? For linear polynomials, this reduces to one version of the classical LittlewoodOfford problem: Given nonzero
The LittlewoodOfford problem and invertibility of random matrices.
 Adv. Math.
, 2008
"... Abstract We prove two basic conjectures on the distribution of the smallest singular value of random n×n matrices with independent entries. Under minimal moment assumptions, we show that the smallest singular value is of order n −1/2 , which is optimal for Gaussian matrices. Moreover, we give a opt ..."
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Cited by 105 (18 self)
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optimal estimate on the tail probability. This comes as a consequence of a new and essentially sharp estimate in the LittlewoodOfford problem: for i.i.d. random variables X k and real numbers a k , determine the probability p that the sum k a k X k lies near some number v. For arbitrary coefficients a k
LittlewoodOfford inequalities for random variables
 11] Nathan Linial, Avner Magen, and Michael
, 1994
"... The concentration of a realvalued random variable X is c(X) sup P(t < X < + 1). Given bounds on the concentrations of n independent random variables, how large can the concentration of their sum be? The main aim of this paper is to give a best possible upper bound for the concentration of the ..."
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Cited by 4 (0 self)
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of the sum of n independent random variables, each of concentration at most 1/k, where k is an integer. Other bounds on the concentration are also discussed, as well as the case of vectorvalued random variables. Key words. LittlewoodOfford problem, concentration, normed spaces AMS subject classifications.
Inverse Littlewood–Offord theorems and the condition number of random discrete matrices
, 2009
"... ..."
Inverse Acoustic and Electromagnetic Scattering Theory, Second Edition
, 1998
"... Abstract. This paper is a survey of the inverse scattering problem for timeharmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering ” and Newtontype methods for solving the inverse scattering problem for acoustic waves, including a brief discussi ..."
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Cited by 1061 (45 self)
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discussion of Tikhonov’s method for the numerical solution of illposed problems. We then proceed to prove a uniqueness theorem for the inverse obstacle problems for acoustic waves and the linear sampling method for reconstructing the shape of a scattering obstacle from far field data. Included in our
Relations defined on sets
 Journal of Formalized Mathematics
, 1989
"... Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse ima ..."
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Cited by 509 (0 self)
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Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse
Results 1  10
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502,619