Renormalization: an advanced overview

We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.Comment: Review, 130 pages, 33 figures; v2: misprints corrected, refs. added, minor improvements; v3: some changes to sect. 5, refs. adde

Higher Order Statistics from the Apm Galaxy Survey

We apply a new statistics, the factorial moment correlators, to density maps obtained from the APM survey. The resulting correlators are all proportional to the two point correlation function, substantially amplified, with an amplification nearly exponential with the total rank of the correlators. This confirms the validity of the hierarchical clustering assumption on the dynamic range examined, corresponding to 0.5 \hmpc - 50 \hmpc in three dimensional space. The Kirkwood superposition with loop terms is strongly rejected. The structure coefficients of the hierarchy are also fitted. The high quality of the APM catalog enabled us to disentangle the various contributions from the power spectrum, small scale nonlinear clustering, and combinatorial effects, all of which affect the amplification of the correlators. These effects should appear in correlations of clusters in a similar fashion.Comment: 30 pages text, 3 pages tables, 5 figures, uuencoded tarred postscrip