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Chernoff Bound

By theoryapp Posted on February 9, 2022 Posted in Probability Tagged with chernoff bound

Consider the sum of a sequence of independent random variables. One may expect its distribution is concentrated around its expected value. This is characterized by the Chernoff bound, which gives exponentially decreasing bounds on tail distributions of the sum. Let …

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Combinatorial Design and Pseudorandom Generator

By theoryapp Posted on December 26, 2020 Posted in Theory Tagged with chernoff bound, combinatorial design, pseudorandom generator

For a set of size \(l\), choose \(m\) subsets each of size \(n\) such that each pair of subsets has intersection size at most \(d\). This gives a combinatorial design with parameters \((m,l,n,d)\). That is, we have \(I_1,\ldots, I_m \subseteq …

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