  In this work, we achieve gap amplification for the Small-Set Expansion
problem. Specifically, we show that an instance of the Small-Set Expansion
Problem with completeness $\epsilon$ and soundness $\frac{1}{2}$ is at least as
difficult as Small-Set Expansion with completeness $\epsilon$ and soundness
$f(\epsilon)$, for any function $f(\epsilon)$ which grows faster than
$\sqrt{\epsilon}$. We achieve this amplification via random walks -- our gadget
is the graph with adjacency matrix corresponding to a random walk on the
original graph. An interesting feature of our reduction is that unlike gap
amplification via parallel repetition, the size of the instances (number of
vertices) produced by the reduction remains the same.
