Capacity, energy and potential theory for random fields

Abstract:

Let $X:\mathbb {R}^N\rightarrow \mathbb {R}^d$ be a random field. We define capacity and energy and obtain a two-sided inequality relating capacity and energy for $X$. We apply our potential-theoretic results to various hitting probabilities for Markov fields. For non-Markovian fields, similar hitting probability results will be given elsewhere.