Overview

Every process in this unit — a Markov chain, a branching process, a Poisson process, a queue — is a generalisation of one idea: a sequence of random values that unfolds one step at a time, where the next step depends on the current position but not on how it was reached. The simple random walk is the cleanest possible instance of that idea, and this topic builds it by hand, using nothing beyond the sums of i.i.d. random variables already available from Probability I. Two genuinely new proof techniques appear here for the first time in the unit — path counting via the reflection principle, and first-step analysis via a difference equation — and both reappear, essentially unchanged, throughout the rest of Probability II.