Logarithmic potential theory and large deviation

Abstract

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 $\mathbf{C}$ with weakly admissible external fields $Q$ and very general measures $\nu$ on $K$. For this we use logarithmic potential theory in ${\mathbf{R}}^n$, $n\ge 2$, and a standard contraction principle in large deviation theory which we apply from the two-dimensional sphere in ${\mathbf{R}}^3$ to the complex plane $\mathbf{C}$.

References in corpus (2)

• Weakly Admissible Vector Equilibrium Problems
• A Note on Large Deviations for 2D Coulomb Gas with Weakly Confining Potential