Suppose $G$ is a random graph on $n$ vertices where each edge appears with probability half. Suppose someone looks at the resulting graph and chooses an arbitrary subset $W$ of vertices of size $k>\sqrt{n}$. How do the eigenvalues of the induced subgraph $G[W]$ behave? In other words can we say that for every $W$ of size $k$, the eigenvalues of $G[W]$ will be close or related to that of a random graph from $G(k,1/2)$?
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