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The relationship between extremum statistics and universal fluctuations

Chapman, Sandra; Rowlands, George; Watkins, Nicholas
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
154.59691%
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the "global" PDF in terms of the "source" PDF of the individual events in the system. A single parameter distinguishes the global PDF and is related to the exponent of the source PDF. When normalized, the global PDF is shown to be insensitive to this parameter and importantly we obtain the previously demonstrated "universality" from an uncorrelated Gaussian source PDF. The second and third moments of the global PDF are more sensitive, providing a powerful tool to probe the degree of complexity of physical systems.; Comment: 6 pages, 1 figure. Paper submitted to PRL, 14th July 2000. Revised version re-submitted to PRL, 12th March, 2001. Paper rejected by PRL. Material herein recast and expanded in form of a new paper (arXiv:cond-mat/0106015), submitted to PRE, 1st June 2001

The pairwise velocity probability density function in models with local primordial non-Gaussianity

Lam, Tsz Yan; Nishimichi, Takahiro; Yoshida, Naoki
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
155.3998%
We study how primordial non-Gaussianity affects the pairwise velocity probability density function (PDF) using an analytical model and cosmological N-body simulations. We adopt the local type non-Gaussian models characterized by f_{nl}, and examine both the linear velocity difference PDF and the linear pairwise velocity PDF. We show explicitly how f_{nl} induces correlations between originally independent velocities along the parallel and the perpendicular to the line of separation directions. We compare the model results with measurements from N-body simulations of the non-Gaussian models. Linear theory fails to predict the PDF in the f_{nl} models. Therefore we develop an analytic model based on the Zeldovich approximation to describe the evolution of the velocity PDF. Our analytical model and simulation results show remarkably good agreement in both the parallel and the perpendicular directions for the PDF profiles, as well as the change in the PDF due to primordial non-Gaussianity. The agreement is particularly good for relatively small separations (< 10 h^{-1} Mpc). The inclusion of the evolution of the velocity PDF is important to obtain a good description on the signature of primordial non-Gaussianity in the PDF. Our model provides the foundation to constrain f_{nl} using the peculiar velocity in future surveys.; Comment: 16 pages...