A Note on Sub-Gaussian Random Variables
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 subGaussians 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.