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

Breakdown of coherence in Kondo alloys: crucial role of concentration vs band filling