标题： 大型非增长网络中度分布的新兴特性 显示英文标题

标题： Emerging properties of the degree distribution in large non-growing networks

摘要： 度分布是网络理论中的一个关键统计指标，常用于理解信息如何在连接的节点之间传播。 在本文中，我们关注通过重连算法形成的非增长网络，并开发了动力学玻尔兹曼型模型，以捕捉表征优先连接网络和随机网络的度分布的出现。 在适当的平均场尺度下，这些模型简化为具有线性扩散系数的福克-普朗克型偏微分方程，这与离散重连过程的一个已建立的主方程一致。 我们进一步分析了这类福克-普朗克方程的平衡收敛性，展示了不同区域——从指数到代数速率——如何依赖于网络参数。 我们的结果为建模非增长网络中的度分布提供了一个统一的框架，并提供了对这类系统长时间行为的见解。 显示英文摘要

摘要： The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and develop kinetic Boltzmann-type models to capture the emergence of degree distributions that characterize both preferential attachment networks and random networks. Under a suitable mean-field scaling, these models reduce to a Fokker-Planck-type partial differential equation with an affine diffusion coefficient, that is consistent with a well-established master equation for discrete rewiring processes. We further analyze the convergence to equilibrium for this class of Fokker-Planck equations, demonstrating how different regimes -- ranging from exponential to algebraic rates -- depend on network parameters. Our results provide a unified framework for modeling degree distributions in non-growing networks and offer insights into the long-time behavior of such systems.