Random Walks

[s pepperchin]

I have been trying to find a good in depth explanation of the math behind random walks ever since it was mentioned in a Quantum Mechanics class I took. If anyone can enlighten me that would be great.

[matt grime]

What's to explain?

 

Let L be a lattice in R^n, that is just the set of coordinates with integer entries, at t=0 you usually start at the origin, and at each time t=n (n in N) you move in any one of the 2n possible directions with equal probability (1/2n). Ie you can't stand still.

 

That's all it is.

 

Perhaps you mean more complicated things like why it is 'recurrent' for n<3 and not otherwise. But that's just probability on n-nomial distributions which sounds far more complicated than it actually is, and is so well known it must be easily googled. Find an explanation on the web (googlefo random walk) and ask about what you don't understand.