Interacting Diffusions on Random Graphs with Diverging Average Degrees: Hydrodynamics and Large Deviations
Interacting Diffusions on Random Graphs with Diverging Average Degrees: Hydrodynamics and Large Deviations
复制标题
具有发散平均度的随机图上的相互作用扩散：流体动力学和大偏差
DOI：
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发表时间：
2018
影响因子：
1.6
通讯作者：
Guilherme Reis
中科院分区：
文献类型：
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作者：
R. Oliveira;Guilherme Reis
我们考虑平均场相互作用的扩散系统，其中成对相互作用的结构由一个稀疏(和潜在的非均匀)随机图来描述。例子包括由ERDőS-Rényi图给出的具有两两相互作用的随机Kuramoto模型。我们的问题是将这类系统的整体行为与具有密集非随机相互作用的相应系统的整体行为进行比较。对于一大类相互作用函数，我们找到了由McKean-Vlasov扩散给出的两个系统具有相同流体动力学极限的最优稀疏条件。此外，我们还证明了两个系统在大偏差水平上的匹配行为。我们的结果推广了Dai Pra和den Hollander的经典结果，并提供了稀疏随机相互作用系统的第一个LDP例子。
We consider systems of mean-field interacting diffusions, where the pairwise interaction structure is described by a sparse (and potentially inhomogeneous) random graph. Examples include the stochastic Kuramoto model with pairwise interactions given by an Erdős–Rényi graph. Our problem is to compare the bulk behavior of such systems with that of corresponding systems with dense nonrandom interactions. For a broad class of interaction functions, we find the optimal sparsity condition that implies that the two systems have the same hydrodynamic limit, which is given by a McKean–Vlasov diffusion. Moreover, we also prove matching behavior of the two systems at the level of large deviations. Our results extend classical results of dai Pra and den Hollander and provide the first examples of LDPs for systems with sparse random interactions.
影响因子：
1.1
作者：
Chiba, Hayato;Medvedev, Georgi S.
通讯作者：
Medvedev, Georgi S.