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math.PR2021★ 3 cited
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…
math.PR2020★ 5 cited
On Chemical Distance and Local Uniqueness of a Sufficiently Supercritical Finitary Random Interlacement
Zhenhao Cai, Xiao Han, Jiayan Ye +1
In this paper, we study geometric properties of the unique infinite cluster in a sufficiently supercritical Finitary Random Interlacements in $\mathbb{Z}^d…
math.PR2020★ 5 cited
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…