Consider a random walker moving in the integers, who jumps to the right with probability p and to the left with probability p, and stays where it is with probability 1-2p . Write the master equation that describes the time evolution of the probability distribution in the system.
Added by Albert J.
Step 1
It can be written as: P(n, t+1) = P(n-1, t) * p + P(n+1, t) * p + P(n, t) * (1-2p) This equation states that the probability of finding the random walker at position n at time t+1 is equal to the sum of three probabilities: Show more…
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