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Unformatted text preview: walk steps (time). Describe the significance of the two terms on the right hand side of the above equation. (b) Calculate the characteristic function G(s,N) for the probability function P(n,N) G ( s , N ) = P ( n , N )exp( ins ) !" " # Assume the particle is at the origin n=0 at N=0. (c) Calculate the average and variance of the random walk using the expression of G(s,N) obtained in part (b). [Interested students can also try the following: Solve the master equation for a simple random walk to obtain an analytical expression for P n,N .] P n , N + 1 = 1 2 P n + 1, N + 1 2 P n ! 1, N...
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- Winter '11