Littlewood-Offord Inequalities for Random Variables
نویسندگان
چکیده
منابع مشابه
Littlewood-Offord Inequalities for Random Variables
The concentration of a real-valued 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 sum of n independent random variables, each of concentration at most 1/k, where k is an integer. Other...
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Let ηi, i = 1, . . . , n be iid Bernoulli random variables, taking values ±1 with probability 1 2 . Given a multiset V of n integers v1, . . . , vn, we define the concentration probability as ρ(V ) := sup x P(v1η1 + . . . vnηn = x). A classical result of Littlewood-Offord and Erdős from the 1940s asserts that, if the vi are non-zero, then ρ(V ) is O(n−1/2). Since then, many researchers have obt...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 1994
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480191221866