  In this note, we study some concentration properties for Lipschitz maps
defined on Hamming graphs, as well as their stability under sums of Banach
spaces. As an application, we extend a result of Causey on the coarse Lipschitz
structure of quasi-reflexive spaces satisfying upper $\ell_p$ tree estimates to
the setting of $\ell_p$-sums of such spaces. Our result provides us with a tool
for constructing the first examples of Banach spaces that are not
quasi-reflexive but nevertheless admit some concentration inequality. We also
give a sufficient condition for a space to be asymptotic-$c_0$ in terms of a
concentration property, as well as relevant counterexamples.
