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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Capacity, energy and potential theory for random fields


Author: Ming Yang
Journal: Trans. Amer. Math. Soc. 366 (2014), 3821-3863
MSC (2010): Primary 60J45, 60G60; Secondary 60G17
Published electronically: February 6, 2014
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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.


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Additional Information

Ming Yang
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: myang1968@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06033-9
PII: S 0002-9947(2014)06033-9
Keywords: Random fields, capacity, energy, potential theory, Markov fields
Received by editor(s): February 13, 2012
Received by editor(s) in revised form: October 13, 2012, and November 10, 2012
Published electronically: February 6, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.