Aspects of Large N Analysis for the Yang-Mills-Higgs Model and Matrix Models

The first part of this work deals with some new large N ideas for the YMH model in three dimensions. Needless to say there is a large historical and scientific background and it is of course difficult to say something really new on these subjects. Nevertheless some latest ideas on matrix models, subject on which I have worked in the first part of my period here at SISSA, are a valuable tool and should find applications in otherwise 'slow' fields. The study of large N model of monopole gas are not investigated, to our knowledge, for example. This work wants to be a starting point for this investigation. Along this analysis we have found many and different problems to think about, the principal is the reason how the Eguchi Kawai works, an issue that also has not been completely clarified, despite of the volume of numerical calculations. After one finds a reliable method for the functional determinant, it will be possible to draw definite conclusions on the large N monopole gas, which seems promising some interesting feature, due to the competition of factors which takes place in the large N limit.