The Four Levels of Fixed-Points in Mean-Field Models

被引:1
作者
Yasodharan, Sarath [1 ]
Sundaresan, Rajesh [1 ,2 ]
机构
[1] Indian Inst Sci, ECE Dept, Bangalore 560012, Karnataka, India
[2] Indian Inst Sci, Robert Bosch Ctr Cyber Phys Syst, Bangalore 560012, Karnataka, India
来源
2021 NATIONAL CONFERENCE ON COMMUNICATIONS (NCC) | 2021年
关键词
Fixed-point; mean-field limit; interacting particle system; performance analysis; McKean-Vlasov equation; propagation of chaos;
D O I
10.1109/NCC52529.2021.9530179
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle systems. These four levels are (i) the macroscopic observables of the system, (ii) the probability distribution over states of a particle at equilibrium, (iii) the time evolution of the probability distribution over states of a particle, and (iv) the probability distribution over trajectories. We then discuss relationships among the fixed-points at these four levels. Finally, we describe some issues that arise in the fixed-point analysis when the system possesses multiple fixed-points at the level of distribution over states, and how one goes beyond the fixed-point analysis to tackle such issues.
引用
收藏
页码:428 / 433
页数:6
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