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We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting scheme under the reasonable (and largely empirically verified) assumption that the long wavelength Fourier components are Gaussian distributed. We apply the formalism to the updated 1-in-6 QDOT IRAS redshift survey, and compare our results to data from other probes: APM angular correlations; the CfA and the Berkeley 1.2Jy IRAS redshift surveys. Our results bear out and further quantify the impression from e.g. counts-in-cells analysis that there is extra power on large scales as compared to the standard CDM model with Ωh ≃ 0.5. We apply likelihood analysis using the CDM spectrum with Ωh as a free parameter as a phenomenological family of models; we find the best fitting parameters in redshift space and transform the results to real space. Finally, we calculate the distribution of the estimated long wavelength power. This agrees remarkably well with the exponential distribution expected for Gaussian fluctuations, even out to powers of ten times the mean. Our results thus reveal no trace of periodicity or other non-Gaussian behavior.

The DEEP2 and COMBO-17 surveys are compared to study luminosity functions of red and blue galaxies to z $ 1. The two surveys have different methods and sensitivities, but nevertheless results agree. After z $ 1, M à B has dimmed by 1.2Y1.3 mag for all colors of galaxies, à for blue galaxies has hardly changed, and à for red galaxies has at least doubled (our formal value is $0.5 dex). Luminosity density j B has fallen by 0.6 dex for blue galaxies but has remained nearly constant for red galaxies. These results imply that the number and total stellar mass of blue galaxies have been substantially constant since z $ 1, whereas those of red galaxies (near L à ) have been significantly rising. To explain the new red galaxies, a ''mixed'' scenario is proposed in which star formation in blue cloud galaxies is quenched, causing them to migrate to the red sequence, where they merge further in a small number of stellar mergers. This mixed scenario matches the local boxy-disky transition for nearby ellipticals, as well as red sequence stellar population scaling laws such as the color-magnitude and Mg-relations (which are explained as fossil relics from blue progenitors). Blue galaxies enter the red sequence via different quenching modes, each of which peaks at a different characteristic mass and time. The red sequence therefore likely builds up in different ways at different times and masses, and the concept of a single process that is ''downsizing'' (or upsizing) probably does not apply. Our claim in this paper of a rise in the number of red galaxies applies to galaxies near L à . Accurate counts of brighter galaxies on the steep part of the Schechter function require more accurate photometry than is currently available.

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