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- W4294344173 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 apply it to obtain a concentration bound for expander random walks which is essentially optimal for small deviations and a large number of steps. At the same time, we present a simpler proof that still yields a right bound settling a question asked by Impagliazzo and Kabanets. Next, we obtain a simple 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 used 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 then show that the same technique yields the upper tail bound for the number of copies of a fixed graph in an ErdH{o}s-R'enyi random graph, matching the one given by Janson, Oleszkiewicz and Ruci'nski (Israel J. Math, 2002)." @default.
- W4294344173 created "2022-09-03" @default.
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- W4294344173 date "2014-05-09" @default.
- W4294344173 modified "2023-09-26" @default.
- W4294344173 title "Upper Tail Estimates with Combinatorial Proofs" @default.
- W4294344173 doi "https://doi.org/10.48550/arxiv.1405.2349" @default.
- W4294344173 hasPublicationYear "2014" @default.
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