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- W2964057862 abstract "We study generalisations of a simple, combinatorial proof of a Chernoff bound similar to the one by Impagliazzo and Kabanets (RANDOM, 2010).In particular, we prove a randomized version of the hitting property of expander random walks and use it to obtain an optimal expander randomwalk concentration bound settling a question asked by Impagliazzo and Kabanets. Next, we obtain an upper tail bound for polynomials with input variables in [0, 1] which are not necessarily independent, but obey a certain condition inspired by Impagliazzo and Kabanets. The resulting bound is applied by Holenstein and Sinha (FOCS, 2012) in the proof of a lower bound for the number of calls in a black-box construction of a pseudorandom generator from a one-way function.We also show that the same technique yields the upper tail bound for the number of copies of a fixed graph in an Erdos–Renyi random graph,matching the one given by Janson, Oleszkiewicz, and Rucinski (Israel J. Math, 2002)." @default.
- W2964057862 created "2019-07-30" @default.
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- W2964057862 date "2015-01-01" @default.
- W2964057862 modified "2023-09-27" @default.
- W2964057862 title "Upper Tail Estimates with Combinatorial Proofs" @default.
- W2964057862 doi "https://doi.org/10.4230/lipics.stacs.2015.392" @default.
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