MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.262 – Discrete Stochastic Processes
Problem Set # 11
Issued:
May 3, 2010
Due:
May 7, 2010
Extensions until May 12 readily granted.
1)
The Voter Problem (Part II).
Consider once again the voter model from Problem 2 in Problem Set #10, defined on a
connected graph
G
with n vertices. Given an initial condition in which each vertex has a
specified opinion (0 or 1), find the probability that the Markov process eventually settles into a
state in which every vertex’s opinion is 1. Though this Markov process has 2
n
states, give an
expression for this probability that can be evaluated for any such graph in at most O(n
2
) steps.
This continues the line of thought we had begun to develop in Problem 2 of Pset #9 and
Problem 2 of Pset #10. However, it seems essentially impossible to solve this without using the
following insight, which we introduce via an example of a 4vertex graph with initial opinions
at the 4 vertices of a, b, c, and d.
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 Spring '08
 Moon,J
 Computer Science, Electrical Engineering, opinion, Stochastic process, Vertex, Markov chain

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