论文标题
在随机图上相互作用的鹰队过程的长期稳定性
Long-term stability of interacting Hawkes processes on random graphs
论文作者
论文摘要
我们考虑了霍克斯的人群，以建模$ n $相互作用的神经元的活动。神经元定期放在节$ [0,1] $上，神经元之间的连通性由随机稀释和不均匀的图给出，其中每个边缘的存在的可能性取决于其通过空间核的人物的空间位置。本文的主要结果涉及人口突触电流的长期稳定性，如$ n \ to \ infty $，如果突触内存内核是指数级，直到$ n $中是多项式的时间范围。
We consider a population of Hawkes processes modeling the activity of $N$ interacting neurons. The neurons are regularly positioned on the segment $[0,1]$, and the connectivity between neurons is given by a random possibly diluted and inhomogeneous graph where the probability of presence of each edge depends on the spatial position of its vertices through a spatial kernel. The main result of the paper concerns the longtime stability of the synaptic current of the population, as $N\to\infty$, in the subcritical regime in case the synaptic memory kernel is exponential, up to time horizons that are polynomial in $N$.
