The size of the longest filament in the Luminous Red Galaxy distribution
  Filaments are one of the most prominent features visible in the galaxy
distribution. Considering the Luminous Red Galaxies (LRGs) in the Sloan Digital
Sky Survey Data Release Seven (SDSS DR7), we have analyzed the filamentarity in
11 nearly two dimensional (2D) sections through a volume limited subsample of
this data. The galaxy distribution, we find, has excess filamentarity in
comparison to a random distribution of points. We use a statistical technique
"Shuffle" to determine $L_{\rm MAX}$, the largest length-scale at which we have
statistically significant filaments. We find that $L_{\rm MAX}$ varies in the
range $100-130 \, h^{-1} {\rm Mpc}$ across the 11 slices, with a mean value
$L_{\rm MAX}=110 \pm 12 \, h^{-1}{\rm Mpc}$. Longer filaments, though possibly
present in our data, are not statistically significant and are the outcome of
chance alignments.
