*Progress in redshift surveys: Left panel (a) it is reported the famous slice of the universe from the CfA2 redhsift survey (De Lapparent, Geller, Huchra, ApJL 302, L1, 1986) in (b) the same sky reagion from the CfA1 catalog (1983) and in (c) the angular Zwicky catalog. Right panel: we show the new SDSS data together with the CfA2 catalog. The famous Great Wall and the new SLOAN Great Wall are clearly visible. In both figures it is reported a small circle of size of 5 Mpc/h, the typical clustering length according to the standard analysis.*

In the past twenty years observations have provided several threedimensional maps of galaxy distribution, from which there is a growing evidence of large scale structures. This important discovery has been possible thanks to the advent of large redshift surveys: angular galaxy catalogs are in fact essentially smooth and structure-less. In the figure above we show a slice of the Center for Astrophysics galaxy catalog (CfA2), which was completed in the early nineties, and a slice constructed from the recent observations of the Sloan Digital Sky Survey (SDSS) project. In the CfA2 catalog, which was one of the first maps surveying the local universe, it has been discovered the giant “Great Wall” a filament linking several groups and clusters of galaxies of extension of about 200 Mpc/h and whose size is limited by the sample boundaries. Recently the SDSS project has reveled the existence of structures larger than the Great Wall, and in particular in the figure above one may notice the so-called “Sloan Great Wall” which is almost double longer than the Great Wall. Nowadays this is the most extended structure ever observed, covering about 400 Mpc/h, and whose size is again limited by the boundaries of the sample.

(The typical mean separation between nearest galaxies is of about 0.1 Mpc. By local universe one means scales in the range [1,100] Mpc/h, where space geometry is basically Euclidean and dynamics is Newtonian, i.e. effects of General Relativity are negligible. On larger scales instead, one has to consider that relativistic corrections start play a role for the determination of the space geometry and dynamics. The size of the universe, according to standard cosmological models is about 5000 Mpc/h, where 1 Mpc = 3 1022 m; distances are given in units of h, a parameter which is in the range [0.5,0.75] reflecting the incertitude in the value of the Hubble constant (H=100 h km/sec/Mpc) used to convert redshift z into distances d~ c/H z (where c is the velocity of light).)

The search for the “maximum” size of galaxy structures and voids, beyond which the distribution becomes essentially smooth, is still an open problem. Instead the fact that galaxy structures are strongly irregular and form complex patterns has become a well-established fact. From the theoretical point of view the understating of the statistical characterization of these structures represents the key element to be considered by a physical theory dealing with their formation. The primary questions that such a situation rises are therefore: (i) which is the nature of galaxy structures and (ii) which is the maximum size of structures ? A number of statistical concepts can be used to answer to these questions: in general one wants to characterize n-point correlation properties which are able to capture the main elements of points distributions.

## Some References

### Books

A. Gabrielli, F. Sylos Labini, M. Joyce and L. Pietronero Statistical physics for cosmic structures Springer-Verlag (2004).

### Review Papers

Yu. V. Baryshev, F. Sylos Labini, M. Montuori and L. Pietronero “Facts and ideas in modern cosmology”, Vistas in Astronomy, 38, No. 4, 419-500, (1994)

F. Sylos Labini, M. Montuori and L. Pietronero “Scale invariance of galaxy clustering” Physics Report, 293, 61-226 (1998)

### Large scale structures

F. Sylos Labini, A. Gabrielli M. Montuori and L. Pietronero “Finite size effects on the galaxy number counts: evidence for fractal behavior up to the deepest scale” Physica A, 266, 195-242 (1996)

H. Di Nella, M. Montuori, G. Paturel, L. Pietronero and F. Sylos Labini “Long-range (fractal) correlations in the LEDA database” Astronom. & Astrophys. Lett 308, L33-L37 (1996)

F. Sylos Labini, M. Montuori and L. Pietronero “Statistical analysis of the Perseus-Pisces redshift survey: spatial and luminosity properties” Physica A, 230, 336-358, (1996)

H. Di Nella & F. Sylos Labini “How can we measure a correlation length of 5-10 Mpc when observations show structures extended over 150 Mpc ?” Astrophys. Lett. and Commun. 36, 33-38 (1997)

F. Sylos Labini, M. Montuori and L. Pietronero “Scaling properties of the Perseus-Pisces redshift survey” Astrophys. Lett. and Commun. 36, 265-271 (1997)

L. Amendola, H. Di Nella, M.Montuori F. Sylos Labini “Statistical properties of galaxy distribution in the LEDA redshift database” Fractals 5, 635-660 (1997)

M. Montuori, F. Sylos Labini and A. Amici “Correlation properties of galaxy cluster distribution” Physica A, 246, 1-17 (1997)

M. Montuori, F. Sylos Labini, A. Gabrielli, A. Amici and L. Pietronero “Galaxy number counts and fractal correlations” Europhysics Letters, 31, 103-108 (1997)

M. Montuori & F. Sylos Labini “Angular correlations of galaxy distribution” Astrophys. J. Letters 487, L21-L24 (1997)

F. Sylos Labini & M. Montuori “Scaling properties of the Stromlo-APM galaxy catalog” Astron. & Astrophys. 331}, 809-814 (1998)

M.Joyce, F. Sylos Labini}, M. Montuori and L. Pietronero “Comment on the paper ‘The ESO Slice Project galaxy redshift survey V. Evidence for a D=3 sample dimensionality’ ” Astron.Astrophys. 344, 387-392, (1999)

M. Joyce, M. Montuori and F. Sylos Labini `Fractal correlations in the The CfA2 -south galaxy redshift survey” Astrophys. Journal Letters, 514, L5-L8, 1999

M. Joyce & F. Sylos Labini “Luminosity density estimation from redshift surveys and the mass density of the Universe” Astrophys. J., 554}, L1-L4, (2001)

H. Di Nella-Courtois, G. Paturel, T. Sousbie, F. Sylos Labini “The LEDA Galaxy distribution: I Maps of the Local Universe” Astron.Astrophys. 423, 27-32 (2004)

F. Sylos Labini “Isotropy, homogeneity and dipole saturation” Astrophys. J. 433, 464-67, (1994)

F. Sylos Labini “Dipole saturation and Large scale structures isotropy” Mem.S.A.it 66 , 267 (1995)

F. Sylos Labini & L. Amendola “The power spectrum in a strongly inhomogeneous Universe” Astrophys.J.Lett., 468 , L1-L4 (1996)

F. Sylos Labini and L. Pietronero “Multifractality as a link between space and luminosity distributions” Astrophys. J., 469 , 28-42 (1996)

F. Sylos Labini and L. Pietronero “Multifractal properties of visible matter” Astrophys. Lett. and Commun. 36 , 49-54 (1996)

F. Sylos Labini and L. Pietronero “Statistical properties of galaxy distributions” Nonlinear process in geophysics, 3 274-283, (1996)

L. Pietronero, M. Montuori and F. Sylos Labini “The debate of galaxy correlations and its theoretical implications” Astrophys. Lett. and Commun. 36 , 65-73 (1997)

F. Sylos Labini & L. Amendola “Power spectrum for fractal distributions” Astrophys. Lett. and Commun. 36 , 59-63 (1997)

R. Durrer, J-P Eckmann, F. Sylos Labini , M. Montuori, and L. Pietronero, Europhys. Lett. 40 , 491-497 (1997)

Y. Baryshev, F. Sylos Labini , M. Montuori, L. Pietronero, and P. Teerikorpi “On the fractal structure of galaxy distribution and its implication for cosmology” Fractals, 6 , 231-244 (1998)

F. Sylos Labini , M. Montuori and L. Pietronero “Multifractality in the large scale distribution of galaxies” Journal de Physique, 8 , 115-118 (1998)

R. Durrer and F. Sylos Labini “A Fractal Galaxy Distribution in a homogeneous universe ?” Astron. Astrophys.Letters 339 , L85-L88 (1998).

A. Gabrielli, F. Sylos Labini and S. Pellegrini “Gravitational force distribution in fractal structures” Europhys.Lett. 46 , 127-133 (1999)

L. Pietronero and F. Sylos Labini “Fractal Universe” , Physica A 280 , 125-130 (2000)

M. Joyce, P. W. Anderson, M. Montuori, L. Pietronero and F. Sylos Labini “Fractal Cosmology in an Open Universe” Europhys.Letters 50 , 416-422 (2000)

A. Gabrielli and F. Sylos Labini “Fluctuations in galaxy counts: a new test for homogeneity versus fractality” Europhysics Letters, 54 , 1, (2001)

L. Pietronero, A. Gabrielli and F. Sylos Labini “Statistical Physics for Cosmic Structures” Physica A, 306 , 395-401 (2002).

F. Sylos Labini & A. Gabrielli “Complexity in cosmic structures” , Physica A, 338 , Issues 1-2, 44-49, (2004).