t-Wise independence with local dependencies

Authors:
Ronen Gradwohl;Amir Yehudayoff
Affiliations:
Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, 76100 Israel;Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, 76100 Israel
Venue:
Information Processing Letters
Year:
2008

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Abstract

In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph G with a bounded chromatic number, in which each vertex represents a random variable. Variables that are represented by neighboring vertices may be arbitrarily dependent, but collections of variables that form an independent set in G are t-wise independent.