具有支撑优势和嵌套混合核的萨雷姆萨科夫型半群
Sarymsakov-Type Semigroups With Support Dominance and Nested Mixing Cores
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中文总结 AI 辅助
本研究针对任意切换下的共识问题，构建三类乘法封闭随机矩阵族，核心为提出含可变混合核维度的几乎萨雷姆萨科夫类，其包含经典萨雷姆萨科夫类且具仅依赖维度的 scramble horizon 界，实例验证了相关假设与界的性质。
中文摘要 AI 辅助
本笔记针对任意切换下的共识问题，构建了三类乘法封闭的随机矩阵族。第一类是对早期幂生成构造的支撑优势扩张，该构造将精确支撑模式匹配放宽为优势型条件，同时不丧失乘法封闭性；第二类是具有精确均匀 scramble horizon 及对应切换乘积收敛速率保证的固定核类；第三类也是主要贡献，是几乎萨雷姆萨科夫类，通过在合适结构条件下允许可变混合核维度得到，该新半群类真包含经典萨雷姆萨科夫类，并具有仅依赖维度的 scramble horizon 界。实例说明了所提结构假设的必要性，并阐明了所得界的尖锐性或局限性。
英文摘要
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.
发表机构
- National Chung Hsing University（中兴大学）
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