基于随机矩阵的复杂系统平衡计数

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2019-10-30 DOI:10.1090/pcms/026/04

Y. Fyodorov

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Counting equilibria in complex systems via random matrices

How many equilibria will a large complex system, modeled by N randomly coupled autonomous nonlinear differential equations typically have? How many of those equilibria are stable, that is are local attractors of the nearby trajectories? These questions arise in many applications and can be partly answered by employing the methods of Random Matrix Theory. The lectures will outline these recent developments. Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom E-mail address: yan.fyodorov@kcl.ac.uk c ©2017 American Mathematical Society

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.