# Random walk with two agents

## Homework Statement

Two drunks start out together at the origin, each having equal probability of making a step to the left or right along the x-axis. Find the probability that they meet again after N steps. It is understood that the men make their steps simultaneously.

## Homework Equations

Binomial theorem. The probability P_N(m) to the single-agent problem is

$$P_N(m) = \frac{N!}{[(N+m)/2]! [(N-m)/2]!} \left(\frac{1}{2}\right)^N \, ;$$

m is the displacement, i.e. n(steps to the right) - n(steps to the left).

## The Attempt at a Solution

I tried considering their relative motion (their separation distance), but had trouble making adjustments to P_N above.

AKG