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A famous Markov chain is the so-called " drunkard's walk ", a random walk on the number line where, at each step, the position may change by + 1 or − 1 with equal probability.
From any position there are two possible transitions, to the next or previous integer.
The transition probabilities depend only on the current position, not on the manner in which the position was reached.
For example, the transition probabilities from 5 to 4 and 5 to 6 are both 0. 5, and all other transition probabilities from 5 are 0.
These probabilities are independent of whether the system was previously in 4 or 6.

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