# a bound on $\|z\|_p$ with high probability for generalized Gaussian vector

Let $$f(x)$$ be the pdf of the generalized Gaussian distribution(GGD), which is given by \begin{align} f(x)=\frac{v}{2\sigma\Gamma(\frac{1}{v})}\exp\left(-\left[\frac{|x|}{\sigma}\right]^{v}\right),~x\in R, \end{align} where $$\sigma>0$$ is a scale parameter, and $$v>0$$ is a shape parameter. The vector $$z\in R^n$$ satisfies independent $$z_i\sim GGD~(i=1,\cdots,n)$$ with $$0. How to provide an explicit bound on $$\|z\|_p~(1 that holds with high probability?