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  3. 3 divide the circle into n points and consider a...

Question: 3 divide the circle into n points and consider a...

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3. Divide the circle into N points, and consider a particle randomly moving between these points, in such a way that the position of the particle is a Markov Chain, and at each step the particle jumps to a neighboring point with equal probabilities 0 Compute P(X,-01X0 = 0) for all n-0. Hint: Use the discrete Fourier transform to diagonalize the transition matrix. That is, express the transition matrix in the orthonor mal basis ê(0),ê(1), , е(N 1) of CN which has the following components in the standard

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