2 typos: sphere->circle. spelling.

Let us call $[A_n,B_n]$ the segment at time $n$. Then, for all $n \ge 1$:

1) $A_n$ is chosen uniformly on the sphere circle of radius $1$ centred at $A_{n-1}$ (independtly independently of the past).

2) $B_n=A_{n-1}$.

Therefore $A_n$ performs a simple random walk.

1

Let us call $[A_n,B_n]$ the segment at time $n$. Then, for all $n \ge 1$:

1) $A_n$ is chosen uniformly on the sphere of radius $1$ centred at $A_{n-1}$ (independtly of the past).

2) $B_n=A_{n-1}$.

Therefore $A_n$ performs a simple random walk.