  We study the low energy states of the Kondo alloy model (KAM) as function of
the magnetic impurity concentration per site, x, and the conduction electron
average site occupation, nc. In previous works, two different Fermi liquid
regimes had been identified at strong Kondo coupling JK, that may be separated
by a transition at x=nc. Here, we analyze the KAM for finite JK on a Bethe
lattice structure. First, using the mean-field coherent potential approximation
(DMFT-CPA) which is exact at lattice coordination Z=infty, we show that the
real part of the local potential scattering may be located outside the
conduction electron band, revealing a possible breakdown of Luttinger 'theorem'
for intermediate values of impurity concentration x. Unusual physical
signatures are expected, e.g., in ARPES experiments. In order to take into
account fluctuations associated with finite dimensionality,i.e., finite Z, we
extend this analyze by also studying the KAM with an adaptation of the
statistical-DMFT method that was developped elsewhere. We review the
distributions of local potential scattering and their evolution with model
parameters: concentration, strength of Kondo coupling, coordination number,
local site neighborhood, connection with percolation issue. Relevence for Kondo
alloys material with f-electrons is also discussed.
