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Math Help - Limiting distribution-Random Walk

  1. #1
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    Limiting distribution-Random Walk

    a) Let
    K5 be the graph with vertices {1,2,3,4,5} and edges {12,13,14,15,23,24,25,34,35,45} (so every pair of vertices are joined). Consider the random walk on K5.
    i) How do you know that this has a unique equilibrium distribution?
    ii) How do you know that it has a limiting distribution?

    iii) Without solving any equations write down the equilibrium distribution.

    thanks for any help.
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  2. #2
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    For i and iii, the symmetry of the graph dictates that each node is the same as every other node. Clearly the equilibrium distribution is the one where each node has 1/5 of the total.
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