  The cutoff phenomenon for an ergodic Markov chain describes a sharp
transition in the convergence to its stationary distribution, over a negligible
period of time, known as cutoff window. We study the cutoff phenomenon for
simple random walks on Kneser graphs, which is a family of ergodic Markov
chains. Given two integers $n$ and $k$, the Kneser graph $K(2n+k,n)$ is defined
as the graph with vertex set being all subsets of $\{1,\ldots,2n+k\}$ of size
$n$ and two vertices $A$ and $B$ being connected by an edge if $A\cap B
=\emptyset$. We show that for any $k=O(n)$, the random walk on $K(2n+k,n)$
exhibits a cutoff at $\frac{1}{2}\log_{1+k/n}{(2n+k)}$ with a window of size
$O(\frac{n}{k})$.
