  A complete representation of the Martin boundary of killed random walks on
the quadrant ${\mathbb{N}}^*\times{\mathbb{N}}^*$ is obtained. It is proved
that the corresponding full Martin compactification of the quadrant
${\mathbb{N}}^*\times{\mathbb{N}}^*$ is homeomorphic to the closure of the set
$\{w={z}/{(1+|z|)}:z\in{\mathbb{N}}^*\times{\mathbb{N}}^*\}$ in
${\mathbb{R}}^2$. The method is based on a ratio limit theorem for local
processes and large deviation techniques.
