The random walk on $R^2$ is defined as infinite series of $\{x_i\}_{i=0}^{\infty}$ where $x_0= (0,0)$ and each move can be one of these vectors: $ \{(-1,0) ,(0,-1) ,(1,0) ,(0,1)\} $
How can I bound the probability I am in a box of $ [-k,k] \times [-k,k]$, i.e. example how can I calculate $\sigma $ if I want to use Chebysehv's?