Logarithmic Potential Theory and Large Deviation

We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets K of C with weakly admissible external fields Q and very general measures ν on K . For this we use logarithmic potential theory in R n , n ≥ 2 , and a standard contraction principle in large deviation theory which we apply from the two-dimensional sphere in R 3 to the complex plane C .