as far back as @tr. We show that neither the statistical model nor the simplest possibility of cannibalism provide a good match for observations, while a more realistic cannibalism scenario works better. Our CLF models both give similar results, in good agreement with observations. Specifically, we find $<m_1>$ between -25 and -25.5 in the K-band, $\sigma(m_1)\sim0.25$ and $<\Delta_{12}>$ between 0.6 and 0.8, for cluster luminosities in the range of $10^{12}$ to $10^{13} h^{-2} 
    {\rm L_\odot}$.
author:
- |
    A. Vale$^{1,2}$[^1] and J. P. Ostriker$^{1,3}$\
    $^{1}$Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom\
    $^{2}$CENTRA, Departamento de Física, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal\
    $^{3}$Princeton University Observatory, Princeton University, Princeton NJ 08544, USA
title: 'The Non-Parametric Model for Linking Galaxy Luminosity with Halo/Subhalo Mass: Are First Brightest Galaxies Special?'
---

galaxies: haloes – galaxies: fundamental parameters – galaxies: clusters: general – dark matter – methods: statistical

Introduction
============

The nature of brightest cluster galaxies (BCGs) has long been a subject of interest and much debate [@peebles; @sandage; @dressler]. In particular, investigators have asked whether their origin is statistical or special in nature, that is, whether they follow a special distribution independent of the 