  The notion of information scrambling is tied to the long-time behaviour of a
system and therefore is related to its infra-red dynamics. In fast scramblers,
information spreads as a logarithmic function of the number of degrees of
freedom. Ordinarily, under an RG-flow, scrambling will become faster in the IR
since many degrees of freedom are integrated out, as a consequence of the
c-theorem. In this article, we consider a class of Holographic quantum field
theories (QFT), which are strongly coupled large $N$ gauge theories with large
number of adjoint and fundamental matter, in which scrambling slows down in the
IR. This happens since more degrees of freedom are inserted in the IR, compared
to the UV, in a precise sense. For generic large $N$ gauge theories, we also
explore general, perturbative flow features of the corresponding Lyapunov
exponent, based on the Callan-Symanzik equation.
