I'm studying statistics and I'm trying to understand markov chain topic. I'm using the package "markovchain" in R to obtain the stationary distribution.
From this transition matrix $M$:
A B A 0.97 0.03 B 0.05 0.95
using the "steadyStates" function I get this:
A B 0.625 0.375
After a few try a noticed that I can obtain the same result if I do this: M^200
So, what I did was to compute 200 matrices using powers from 1 to 200 to show how each element in the matrix changes after every iteration (e.g. how 0.97 becomes 0.625 and 0.03 becomes 0.375). Then I plotted these 4 vectors (with 200 entries each) in 4 separate plots (I'm attaching the two types of plot I got here below).
My questions are:
Does it makes any sense to plot these values?
Can I get some insight from them? For example, can I interpret these plots like some sort of a "elbow method"? Or maybe something like: after 50 iteration I have a good approximation of the final values...
If I use two or more matrices can I say: matrix one "converges" before matrix two, three, etc.?
Thank you for your time.