Email Gateway (Jan 20 2025 at 09:21): Email Gateway (Jan 20 2025 at 09:21):From: Tobias Nipkow <nipkow@in.tum.de>
Enjoy another exciting contribution by Emin Karayel:
Negatively Associated Random Variables
Negative Association is a generalization of independence for random variables,
that retains some of the key properties of independent random variables. In
particular closure properties, such as composition with monotone functions, as
well as, the well-known Chernoff-Hoeffding bounds. This entry introduces the
concept and verifies the most important closure properties, as well as, the
concentration inequalities. It also verifies the FKG inequality, which is a
generalization of Chebyshev's sum inequality for distributive lattices and a key
tool for establishing negative association, but has also many applications
beyond the context of negative association, in particular, statistical physics
and graph theory. As an example, permutation distributions are shown to be
negatively associated, from which many more sets of negatively random variables
can be derived, such as, e.g., n-subsets, or the the balls-into-bins process.
Finally, the entry derives a correct false-positive rate for Bloom filters using
the library.
https://www.isa-afp.org/entries/Negative_Association.html
Last updated: Jan 30 2025 at 04:21 UTC