0000000000728337
AUTHOR
Vicent J. Martinez
Introductory review to the historical development of modern cosmology
This talk introduces the contributions of the lecturers to the international summer school ``Historical Development of Modern Cosmology'' held at the Universidad Internacional Men\'endez Pelayo, Valencia, Spain, during September 18-22 2000.
The Large Scale Structure in the Universe: From Power-Laws to Acoustic Peaks
The most popular tools for analysing the large scale distribution of galaxies are second-order spatial statistics such as the two-point correlation function or its Fourier transform, the power spectrum. In this review, we explain how our knowledge of cosmic structures, encapsulated by these statistical descriptors, has evolved since their first use when applied on the early galaxy catalogues to the present generation of wide and deep redshift surveys, incorporating the most challenging discovery in the study of the galaxy distribution: the detection of Baryon Acoustic Oscillations.
Multiscaling
We introduce the unbiased way statisticians look at the 2--point correlation function and study its relation to multifractal analysis. We apply this method to a simulation of the distribution of galaxy clusters in order to check the dependence of the correlation dimension on the cluster richness.
Measures of the galaxy clustering
A brief introduction is given to some aspects of the statistical description of the luminous matter distribution. I review the features of the redshift surveys that arise in the statistical analysis of the galaxy clustering. Special topics include intensity functions, correlation functions, correlation integrals, multifractals and multiscaling.