Statistically significant length scale of filaments as a robust measure
  of galaxy distribution
  We have used a statistical technique "Shuffle" (Bhavsar & Ling 1988;
Bharadwaj, Bhavsar & Sheth 2004) in seven nearly two dimensional strips from
the Sloan Digital Sky Survey Data Release Six (SDSS DR6) to test if the
statistically significant length scale of filaments depends on luminosity,
colour and morphology of galaxies. We find that although the average
filamentarity depends on these galaxy properties, the statistically significant
length scale of filaments does not depend on them. We compare it's measured
values in SDSS against the predictions of Lambda CDM N-body simulations and
find that Lambda CDM model is consistent with observations. The average
filamentarity is known to be very sensitive to the bias parameter. Using Lambda
CDM N-body simulations we simulate mock galaxy distributions for SDSS NGP
equatorial strip for different biases and test if the statistically significant
length scale of filaments depends on bias. We find that statistically
significant length scale of filaments is nearly independent of bias. The
average filamentarity is also known to be dependent on the galaxy number
density and size of the samples. We use Lambda CDM dark matter N-body
simulations to test if the statistically significant length scale of filaments
depends on these factors and find a very weak dependence. Finally we test the
reliability of our method by applying it to controlled samples of segment Cox
process and find that our method successfully recovers the length of the
inputted segments. Summarizing these results we conclude that the statistically
significant length scale of filaments is a robust measure of the galaxy
distribution.
