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PreprintCC BY 4.0arXiv

Sarymsakov-Type Semigroups With Support Dominance and Nested Mixing Cores

  • Shun-Pin Hsu
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Abstract

This note develops three multiplication-closed families of stochastic matrices for consensus under arbitrary switching. The first is a support-dominance enlargement of an earlier power-generated construction, in which exact support-pattern matching is relaxed to a dominance-type condition without losing closure under multiplication. The second is a fixed-core class with an exact uniform scrambling horizon and corresponding convergence-rate guarantees for switching products. The third and main contribution is the almost Sarymsakov class, obtained by allowing variable mixing-core dimensions under suitable structural conditions. This new semigroup class properly contains the classical Sarymsakov class and admits a dimension-only scrambling-horizon bound. Examples illustrate the necessity of the proposed structural assumptions and clarify the sharpness or limitations of the derived bounds.

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Cite

BibTeXRIS
BibTeX
@misc{hsu2026sarymsakovtype,
  title = {{Sarymsakov-Type Semigroups With Support Dominance and Nested Mixing Cores}},
  author = {Shun-Pin Hsu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05050},
  eprint = {2609.05050},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05050},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sarymsakov-Type Semigroups With Support Dominance and Nested Mixing Cores
AU  - Shun-Pin Hsu
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05050
UR  - https://arxiv.org/abs/2609.05050
AB  - This note develops three multiplication-closed families of stochastic matrices for consensus under arbitrary switching. The first is a support-dominance enlargement of an earlier power-generated construction, in which exact support-pattern matching is relaxed to a dominance-type condition without losing closure under multiplication. The second is a fixed-core class with an exact uniform scrambling horizon and corresponding convergence-rate guarantees for switching products. The third and main contribution is the almost Sarymsakov class, obtained by allowing variable mixing-core dimensions under suitable structural conditions. This new semigroup class properly contains the classical Sarymsakov class and admits a dimension-only scrambling-horizon bound. Examples illustrate the necessity of the proposed structural assumptions and clarify the sharpness or limitations of the derived bounds.
ER  -