A class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree

2019 ◽  
pp. 1-18 ◽  
Author(s):  
Pingping Zhong ◽  
Zhiyan Shi ◽  
Weiguo Yang ◽  
Fan Min
Keyword(s):  
Markov Chains ◽  
Random Fields ◽  
Binary Tree ◽  
Strong Deviation

Markov Chains in Many Dimensions

1994 ◽  
Vol 26 (3) ◽  
pp. 756-774 ◽  
Author(s):  
Dimitris N. Politis
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Maximum Entropy ◽  
Stationary Distribution ◽  
Random Fields ◽  
Special Class ◽  
Markov Random Fields ◽  
One Dimension ◽  
Stationary Markov Chain ◽  
Markov Random

A generalization of the notion of a stationary Markov chain in more than one dimension is proposed, and is found to be a special class of homogeneous Markov random fields. Stationary Markov chains in many dimensions are shown to possess a maximum entropy property, analogous to the corresponding property for Markov chains in one dimension. In addition, a representation of Markov chains in many dimensions is provided, together with a method for their generation that converges to their stationary distribution.

Mathematics and Innovation in Engineering

2008 ◽  
Vol 380 ◽  
pp. 3-14
Author(s):  
Elena Beretta ◽  
Alberto Gandolfi ◽  
C.C.A. Sastri
Keyword(s):  
Markov Chains ◽  
Large Deviations ◽  
Random Fields ◽  
Spin Glasses ◽  
Markov Random Fields ◽  
Imaging Technologies ◽  
Inverse Conductivity Problem ◽  
Markov Random ◽  
The Way ◽  
Conductivity Problem

We present some examples of mathematical discoveries whose original import was mainly theoretical but which later ended up triggering extraordinary ad- vances in engineering, sometimes all the way down to technological realizations and market products. The examples we cite include Markov chains and Markov random fields, spin glasses, large deviations and the inverse conductivity problem, and their effects in various areas such as communication and imaging technologies.

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