  We define a class of random matrix ensembles that pertain to random looped
polymers. Such random looped polymers are a possible model for bio-polymers
such as chromatin in the cell nucleus. It is shown that the distribution of the
largest eigenvalue $\lambda_{max}$ depends on a percolation transition in the
entries of the random matrices. Below the percolation threshold the
distribution is multi-peaked and changes above the threshold to the Tracy-Widom
distribution. We also show that the distribution of the eigenvalues is neither
of the Wigner form nor gaussian.
