Logarithmic potential theory and large deviation

Thomas Bloom (1) , Norman Levenberg (2) , Franck Wielonsky (3)

1 University of Toronto
2 Indiana University [Bloomington]
3 I2M - Institut de Mathématiques de Marseille

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. 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.

Domaines: Probabilités [math.PR]

Thomas Bloom, Norman Levenberg, Franck Wielonsky. Logarithmic potential theory and large deviation. Computational Methods and Function Theory, 2015, 15 (4), pp.555-594. ⟨10.1007/s40315-015-0120-4⟩. ⟨hal-01266133⟩