On the carrying dimension of occupation measures for self-affine random fields
Probability
2021-06-15 v1
Abstract
Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for the sample functions of a large class of self-affine random fields. We present a close relationship between the carrying dimension of the corresponding self-affine random occupation measure introduced by U. Z\"ahle and the Hausdorff dimension of the graph of self-affine fields. In the case of exponential scaling operators, the dimension formula can be explicitly calculated by means of the singular value function. This also enables to get a lower bound for the Hausdorff dimension of the range of general self-affine random fields under mild regularity assumptions.
Keywords
Cite
@article{arxiv.1705.05676,
title = {On the carrying dimension of occupation measures for self-affine random fields},
author = {Peter Kern and Ercan Sönmez},
journal= {arXiv preprint arXiv:1705.05676},
year = {2021}
}