4ae67a7dd7e491f8fb6f9ea0cf25dfdb-Supplemental.pdf

In this paper, we need a sequence of random variables{Xn}n 1 such that Xn N(0,σ2n), limn + σn = 0, and Xn 0 almost surely. The following lemma shows the existence of suchasequence. It follows thatrank(M) rank(M1)+rank(M2) = 2. The matrixM has at leastn 2 zero eigenvalues. We have shown thatM has eigenvalue1 1/z and M has at most two non-zero eigenvalues. This is indeed possibleas we immediatelyshow.