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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

A random walk on the path graph with vertices 1−2−3−41 - 2 - 3 - 4 moves each step to a uniformly random neighbour of its current vertex. The steady state of a random walk on a graph is proportional to vertex degree. What is the steady-state probability of vertex 1? Express your answer as a common fraction.