can anyone give an example of a physical system(phenomena) that often arises in the field of engineering research whose states-space has to be taken as a complete separable metric space(I precisely do not want compact metric space), and that system can be modeled as a discrete-time Markov chain?
2026-03-29 17:31:41.1774805501
example of a physical phenomenon
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Queues in queueing theory: the system is modeled using a discrete-time Markov chain, where the state of the queue is the number of elements in the system
Harchol-Balter, M. (2013). Performance modeling and design of computer systems: queueing theory in action. Cambridge University Press.
Ising model, in Physics: it is used in Engineering research and machine learning to remove noise from images
Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.
section 8.3.3
https://en.wikipedia.org/wiki/Ising_model
https://en.wikipedia.org/wiki/Ising_model#Viewing_the_Ising_model_as_a_Markov_chain
https://github.com/AmazaspShumik/BayesianML-MCMC/blob/master/Gibbs%20Ising%20Model/imageDenoisingExample.m