All Questions

I know that many things are known when dealing with random walks on a finite (or even infinite) graph: mixing time, returns to origin, etc. All is based in the use of the Markovian property of such a ...

The high-level question is: can we generate any random graph with size $d$ using a Markov chain? For example, let $X^{(0)} = (1,0,\ldots,0) \in R^d$ be the initial state, and $X^{(t+1)} = f^{(t)}(X^{...

I have spent a lot of time trying to solve this problem but have had no luck so far! Any help would be highly appreciated! Suppose I have a 3x3 grid as shown below. (3,1) (3,2) (3,3) (2,1) (2,2) (...