Aspects of large random Markov kernels

作者：Chafai Djalil^*

来源：Stochastics: An International Journal of Probability and Stochastic Processes , 2009, 81(3-4): 415-429.

DOI：10.1080/17442500903080314

• random matrices
• finite graphs
• convex polytopes
• symmetric group
• Markov chains
• invariant measures

We briefly review certain asymptotic properties of random Markov kernels on a finite state space. These models can be thought of as finite Markov chains in random environment. Here, the asymptotics are taken with respect to the cardinality of the state space. We study, for instance, the behaviour of the normalized invariant vector, the global behaviour of the spectrum and the extremal eigenvalues. The analysis of these models involves Random Matrix Theory, convex compact polytopes and finite graphs with random weights. We also give some open problems related to these models.

• 出版日期2009