Can anyone provide some motivation behind the use of random walks? I know they're used a lot in computer science, in things like page walk (I think that's what it was called- something like pagerank), but they are also used to model things like brownian motion- and I just don't understand why they are so useful. Is it just because they are the way to model randomness? Is there some larger theory behind random walks, or are they a very simple concept? Initially I had begun to look at quantum random walks for algorithms, and I couldn't see the use of quantum random walks-so I looked at classical random walks.
For instance, I've heard about random walks in things like search algorithms, but is that really more useful than just searching the whole data structure?