A subgaussian random variable is a real random variable 
whose tail probabilities decay at least as fast as
a Gaussian, up to rescaling. One equivalent
convention requires some 
such that
 |
where 
denotes expectation value. Markov's
inequality then gives 
for 
. The parameter 
depends on the chosen normalization.
A centered random vector 
is linearly 
-subgaussian in this convention when every unit
vector 
satisfies
 |
This bounds all scalar projections using the same 
.
