198 citations
- Duke UniversityUS37 papers
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- A. Alikhanyan National LaboratoryAM2 papers
- Brookhaven National LaboratoryUS2 papers
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- Chinese Academy of SciencesCN2 papers
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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…
math.PR2017★ 3 cited
Average nearest neighbor degrees in scale-free networks
Dong Yao, Pim van der Hoorn, Nelly Litvak
The average nearest neighbor degree (ANND) of a node of degree is widely used to measure dependencies between degrees of neighbor nodes in a network. We formally analyze ANND i…
math.PR2015★ 1 cited
Convergence of Stochastic Interacting Particle Systems in Probability under a Sobolev Norm
Jian-Guo Liu, Yuan Zhang
In this paper, we consider particle systems with interaction and Brownian motion. We prove that when the initial data is from the sampling of Chorin's method, i.e., the initial ver…