Question: Problem 5.8. Consider a random walk on the lattice shown in Fig. 5.6. The site, P, absorbs the walker. The transition rates are w,2 =

Problem 5.8. Consider a random walk on the lattice shown in Fig. 5.6. The site, P, absorbs the walker. The transition rates are w,2 = w13 =, w21 =W2,3=w2.p=}, w3,1 = w3,2 = w3,p = , and wp1=wp2 =

(a) Write the transition matrix, M, and compute its eigenvalues and and left and right eigenvectors.

(b) If the walker starts at site n 1 at time t = 0, compute the mean first passage time.

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