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Title:
A Note on Sub-Gaussian Random Variables
Authors: Benjamin M. Case, Colin Gallagher, Shuhong Gao
Abstract:A sub-Gaussian distribution is any probability distribution that has tails bounded by a Gaussian and has a mean of zero. It is well known that the sum of independent sub-Gaussians is again sub-Gaussian. This note generalizes this result to sums of sub- Gaussians that may not be independent, under the assumption a certain conditional distribution is also sub-Gaussian. This general result is useful in the study of noise growth in (fully) homomorphic encryption schemes [CGHX19, CGGI17], and hopefully useful for other applications.
ePrint: https://eprint.iacr.org/2019/520
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