Question

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: 2 2 0 N- 1 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 (0), ê(1) . ., є(N-1) of CN which has the following components in the standard

Answer 1

3. Divide the circle into N point, and consider a particle randomly moving between these points, in such a way that the position of the particle is a Markov Clain, and at each step the particle jumps to a neighbouring point with equal probabilities: