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A mean-field approach to self-interacting networks, convergence and regularity
Mathematical Models and Methods in Applied Sciences ( IF 3.5 ) Pub Date : 2021-11-24 , DOI: 10.1142/s0218202521500573
Rémi Catellier 1 , Yves D’Angelo 1 , Cristiano Ricci 2
Affiliation  

The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the generality of the modeling choices are discussed. Convergence of the empirical density for the particle system to its mean-field limit is proved, and a result of regularity for the solution is presented.

中文翻译:

自交互网络、收敛性和规律性的平均场方法

研究了相互作用粒子系统的混沌特性的传播,描述了相互作用细丝网络的空间演化。以菌丝体网络的建立为代表案例进行了分析,并讨论了建模选择的一般性。证明了粒子系统的经验密度与其平均场极限的收敛性,并给出了解的规律性结果。
更新日期:2021-11-24
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