Consider a random process $X=X_1,X_2,\ldots X_n$ such that $X_0=0^d$ and $\forall i:X_i\in\mathbb R^d$.
For $i\ge 1$, The value of $X_i$ is determined by moving a ($\ell_2$) distance of (exactly) $1$, in a random direction, from $X_{i-1}$.
What is $\mathbb E[|X_n|]$ - the expected ($\ell_2$) distance the process makes from the origin?
Obviously, for $d=1$ this is a standard 1D integer random walk and we have $\mathbb E[|X_n|]=O(\sqrt n)$.