重尾网络上的强迫凝聚和抗凝聚
Allocation Condensation in Redistributive Networks
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中文总结 AI 辅助
研究重尾网络上的驱动选择机制，通过幂归一化规则等确定质量传输方向，指数θ控制反馈。此机制区分了多种效应，正、负反馈分别选择高低响应节点，有限幂律网络实验支持相关结果，该机制与其他机制不同，能选择非平衡分布。
中文摘要 AI 辅助
我们研究了固定重尾网络上的驱动选择机制。每一步注入新质量，其方向通过幂归一化规则根据当前质量分布重新计算，组合质量由原始混合矩阵传输。指数θ控制反馈，正值更看重较大坐标，负值则相反，θ = 0时质量均匀分布。排除总质量的确定性增长后，长期注入分布由单纯形上的非线性Perron - Frobenius不动点表征。通过希尔伯特投影度量理解系统稳定性，折扣网络响应使正分布更接近，伴护映射按|θ|缩放投影距离。在重尾网络上，此不动点区分了常被混淆的三种效应：响应或度倾斜、反常逆参与率缩放和真正的少数节点定位。正反馈选择高响应节点，负反馈选择低响应节点。有限幂律网络的数值实验支持这些结果，展示了收敛性等。该机制不同于守恒质量凝聚和图增长，而是在固定的异质网络上通过反馈选择非平衡分布。
英文摘要
We study a fixed network on which new mass is allocated in proportion to a power of each node's stock and then redistributed. Transport retains a fraction of both old and new mass at each node and divides the rest according to fixed background shares. We show that a small amount of retention can sustain concentration on networks where complete redistribution would leave every node's share of new mass vanishing as the network grows. A node receiving most new mass may retain little relative to the network total, yet much more than redistribution alone would supply. For a power above one, the allocation rule amplifies this relative stock advantage at the next step. We identify retention rates tending to zero with network size that allow widely spread and concentrated stationary allocations to coexist on the same network. One of them stays close to the allocation under complete redistribution. Each node can also dominate a separate concentrated allocation, receiving a share of new mass tending to one. The stocks supporting these allocations attract nearby trajectories, although every stationary stock approaches the same background, with even its largest share tending to zero. These allocations continue to coexist under specified changes in transport that preserve the background. Redistribution can therefore spread the stock widely without spreading new allocations in the same way.
发表机构
- Indian Institute of Management Kozhikode（印度科泽科德管理学院）
机构由 AI 辅助整理，请以论文原文为准。
