  The dynamics of a subdiffusive continuous time random walker in an
inhomogeneous environment is analyzed. In each microscopic jump, a random time
is drawn from a waiting time probability density function (WT-PDF) that decays
as a power law: phi(t;k)~k/(1+kt)^(1+beta), 0<beta<1. The parameter k, which is
the diffusion coefficient for the jump, is a random quantity also; in each
jump, it is drawn from a PDF, p(k)~1/k^gamma (0<gamma<1). We show that this
system exhibits a transition in the scaling law of its effective WT-PDF,
psi(t), which is obtained when averaging phi(t;k) with p(k). psi(t) decays as a
power law, psi(t)~1/t^(1+mu), and mu is given by two different formula. When
1-gamma> beta;, mu=beta, but when 1-gamma<beta, mu=1-gamma. The transition in
the scaling of psi(t) reflects the competition between two different mechanisms
for subdiffusion: subdiffusion due to the heavily tailed phi(t;k) for
microscopic jumps, and subdiffusion due to the collective effect of an
environment made of many slow local regions. These two different mechanisms for
subdiffusion are not additive, and compete each other. The reported transition
is dimension independent, and disappears when the power beta is also
distributed, in the range, 0<bate<1. Simulations exemplified the transition,
and implications are discussed.
