论文标题
马尔可夫流程的大量人口限制在随机网络上
Large population limits of Markov processes on random networks
论文作者
论文摘要
我们考虑在相互作用剂的随机网络上进行时间连续的马尔可夫离散状态动力学，并研究较大的人口限制。该动力学被投影到系统中每个离散状态或某些子系统中的股份给出的低维集体变量上，并证明了集体变量动力学与平均范围普通微分方程的一般条件。我们讨论了在Erdős-rényi随机图，随机块模型和随机常规图上的连续时噪声版本和在ERDőS-Rényi随机图上的连续时间噪声版本的收敛。此外，还研究了异质人群。
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called ``voter model'' on Erdős-Rényi random graphs, on the stochastic block model, and on random regular graphs. Moreover, a heterogeneous population of agents is studied.
