  This paper shows how to solve linear programs of the form $\min_{Ax=b,x\geq0}
c^\top x$ with $n$ variables in time
$$O^*((n^{\omega}+n^{2.5-\alpha/2}+n^{2+1/6}) \log(n/\delta))$$ where $\omega$
is the exponent of matrix multiplication, $\alpha$ is the dual exponent of
matrix multiplication, and $\delta$ is the relative accuracy. For the current
value of $\omega\sim2.37$ and $\alpha\sim0.31$, our algorithm takes
$O^*(n^{\omega} \log(n/\delta))$ time. When $\omega = 2$, our algorithm takes
$O^*(n^{2+1/6} \log(n/\delta))$ time.
  Our algorithm utilizes several new concepts that we believe may be of
independent interest:
  $\bullet$ We define a stochastic central path method.
  $\bullet$ We show how to maintain a projection matrix
$\sqrt{W}A^{\top}(AWA^{\top})^{-1}A\sqrt{W}$ in sub-quadratic time under
$\ell_{2}$ multiplicative changes in the diagonal matrix $W$.
