101,119 research outputs found
Measuring non-linear dependence for two random variables distributed along a curve
The final publication is available at link.springer.comWe propose new dependence measures for two real random variables not necessarily linearly related. Covariance and linear correlation are expressed in terms of principal components and are generalized for variables distributed along a curve. Properties of these measures are discussed. The new measures are estimated using principal curves and are computed for simulated and real data sets. Finally, we present several statistical applications for the new dependence measures.Peer ReviewedPostprint (author's final draft
Measuring nonlocal Lagrangian peak bias
We investigate nonlocal Lagrangian bias contributions involving gradients of
the linear density field, for which we have predictions from the excursion set
peak formalism. We begin by writing down a bias expansion which includes all
the bias terms, including the nonlocal ones. Having checked that the model
furnishes a reasonable fit to the halo mass function, we develop a 1-point
cross-correlation technique to measure bias factors associated with
2-distributed quantities. We validate the method with numerical realizations of
peaks of Gaussian random fields before we apply it to N-body simulations. We
focus on the lowest (quadratic) order nonlocal contributions. We can reproduce
our measurement of \chi_{10} if we allow for an offset between the Lagrangian
halo center-of-mass and the peak position. The sign and magnitude of \chi_{10}
is consistent with Lagrangian haloes sitting near linear density maxima. The
resulting contribution to the halo bias can safely be ignored for M = 10^13
Msun/h, but could become relevant at larger halo masses. For the second
nonlocal bias \chi_{01} however, we measure a much larger magnitude than
predicted by our model. We speculate that some of this discrepancy might
originate from nonlocal Lagrangian contributions induced by nonspherical
collapse.Comment: (v2): presentation clarified. agreement with the simulation improved.
accepted for publication. 11 pages, 8 figure
Growing dynamical length, scaling and heterogeneities in the 3d Edwards-Anderson model
We study numerically spatio-temporal fluctuations during the
out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model.
We focus on two issues. (1) The evolution of a growing dynamical length scale
in the glassy phase of the model, and the consequent collapse of the
distribution of local coarse-grained correlations measured at different pairs
of times on a single function using {\it two} scaling parameters, the value of
the global correlation at the measuring times and the ratio of the coarse
graining length to the dynamical length scale (in the thermodynamic limit). (2)
The `triangular' relation between coarse-grained local correlations at three
pairs of times taken from the ordered instants .
Property (1) is consistent with the conjecture that the development of
time-reparametrization invariance asymptotically is responsible for the main
dynamic fluctuations in aging glassy systems as well as with other mechanisms
proposed in the literature. Property (2), we stress, is a much stronger test of
the relevance of the time-reparametrization invariance scenario.Comment: 24 pages, 12 fig
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