173Discussion5 - Discussion 5 Mariana Olvera-Cravioto UC...

This preview shows page 1 - 5 out of 11 pages.

Discussion 5Mariana Olvera-CraviotoUC Berkeley[email protected]February 17th, 2017IND ENG 173, Introduction to Stochastic ProcessesDiscussion 51/8
Example: more random walks on graphsIConsider the following undirected graph:126735432241321ILetwijdenote the “weight” on the edge(i, j).ILetXnbe the current vertex after thenth transition.IND ENG 173, Introduction to Stochastic ProcessesDiscussion 52/8
Random walk on a graph... continuedISuppose the transition probabilities are such thatp(i, j) =wijkwik,i.e., we move from vertexito vertexjwith a probability proportional tothe edge’s weight.IFor our graph in particular, the transition matrix is:P=03/83/802/8003/5000002/500002/2003/4000001/42/802/8004/8000004/501/502/401/401/40IND ENG 173, Introduction to Stochastic ProcessesDiscussion 53/8
Setting up the detailed balance equationsIThe time reversibility equations in this case are:xiwij

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture