Vector Energy and Large Deviation
Complex Variables
2013-01-08 v1 Classical Analysis and ODEs
Probability
Abstract
For d nonpolar compact sets K_1,...,K_d in the complex plane, d admissible weights Q_1,...,Q_d, and a positive semidefinite d x d interaction matrix C with no zero column, we define natural discretizations of the associated weighted vector energy of a d-tuple of positive measures \mu=(\mu_1,...,\mu_d) where \mu_j is supported in K_j and has mass r_j. We have an L^{\infty}-type discretization W(\mu) and an L^2-type discretization J(\mu) defined using a fixed measure \nu=(\nu_1,...,\nu_d). This leads to a large deviation principle for a canonical sequence of probability measures on this space of d-tuples of positive measures if \nu=(\nu_1,...,\nu_d) is a strong Bernstein-Markov measure.
Cite
@article{arxiv.1301.1095,
title = {Vector Energy and Large Deviation},
author = {T. Bloom and N. Levenberg and F. Wielonsky},
journal= {arXiv preprint arXiv:1301.1095},
year = {2013}
}