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PreprintCC BY-NC-ND 4.0HAL

Random self-similar series on the two-dimensional torus

  • Julien Brémont
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Abstract

We study real random self-similar series defined on the two-dimensional torus equipped with an ergodic translation and Lebesgue measure. Supposing the data piecewise constant on a polygonal partition, we provide sufficient conditions for the occupation measure to be continuous and zero Box-dimensional.

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Cite

BibTeXRIS
BibTeX
@misc{bremont2026random,
  title = {{Random self-similar series on the two-dimensional torus}},
  author = {Julien Brémont},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05622557v2},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Random self-similar series on the two-dimensional torus
AU  - Julien Brémont
PY  - 2026
DA  - 2026/09/09
PB  - HAL
UR  - https://hal.science/hal-05622557v2
AB  - We study real random self-similar series defined on the two-dimensional torus equipped with an ergodic translation and Lebesgue measure. Supposing the data piecewise constant on a polygonal partition, we provide sufficient conditions for the occupation measure to be continuous and zero Box-dimensional.
ER  -