首页    期刊浏览 2025年07月11日 星期五
登录注册

文章基本信息

  • 标题:Toward a Theory of Markov Influence Systems and their Renormalization
  • 作者:Bernard Chazelle
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2018
  • 卷号:94
  • 页码:58:1-58:18
  • DOI:10.4230/LIPIcs.ITCS.2018.58
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:Nonlinear Markov chains are probabilistic models commonly used in physics, biology, and the social sciences. In "Markov influence systems" (MIS), the transition probabilities of the chains change as a function of the current state distribution. This work introduces a renormalization framework for analyzing the dynamics of MIS. It comes in two independent parts: first, we generalize the standard classification of Markov chain states to the dynamic case by showing how to "parse" graph sequences. We then use this framework to carry out the bifurcation analysis of a few important MIS families. In particular, we show that irreducible MIS are almost always asymptotically periodic. We also give an example of "hyper-torpid" mixing, where a stationary distribution is reached in super-exponential time, a timescale that cannot be achieved by any Markov chain.
  • 关键词:Markov influence systems; nonlinear Markov chains; dynamical systems; renormalization; graph sequence parsing
Loading...
联系我们|关于我们|网站声明
国家哲学社会科学文献中心版权所有