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Column stochastic matrix/Ring/6/Both directions/Exercise

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Let a circle with six (equidistant) points be given, denoted by 1,2,3,4,5,6. We look at a movement process where the probabilities to stay at the current position and to change to the neighbor on the left or on the right equal 13. Establish the corresponding stochastic matrix, and compute the eigendistribution(s).