What is Reddit's opinion of Stochastic Methods (Springer Series in Synergetics, 13)?

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Are you interested in the discrete or continuum case? Do you only care about being a certain distance away or do you care about position?

In the discrete case, look up master equations (for random walks). There's tons of resources on the derivations in 1d, and the extension to 2d is not much more complicated. Instead of having a recurrence relation for P(x,n), you'll have one for P(x,y,n), where P is the probability of being at location x (or x and y) at step n.

The continuum case gives you Brownian motion or some other stochastic process, depending how you set up your master equation. I think the 1d case has an explicit formula for calculating first passage times (which you could then marginalize over for distance). However, non-standard 2d walks are still open topics of research for the most part. Benichou has done a lot of work on this and has a good overview paper on calculating and estimating these things.

If you want a reference on derivations of these first passage times, you'll need to know things like the Fokker-Planck equation. Gardiner is a pretty good reference for these things.