Randomized findings show concentration of variables via Hoeffding's lemma, indicating dependence effects.
Key Points
This research aims to explore the concentration of certain variables using a tensorization of Hoeffding’s lemma, particularly in high-dimensional settings.
Examined the concentration of the Hamming metric in product distributions on the Boolean cube.
Developed bounds on the exponential moment generating function and characterized concentration through correlation conditions.
Extended results to finite, discrete sample spaces and utilized Markov’s inequality for dependent random variables.
Established concentration of the Hamming metric for product distributions, independent of the fixed point.
Identified dependency effects leading to failure in concentration for certain distributions.
Provided a comprehensive framework that simplifies the bounding process for sums of random variables.