ترغب بنشر مسار تعليمي؟ اضغط هنا

Linear theory and velocity correlations of clusters

55   0   0.0 ( 0 )
 نشر من قبل Ravi K. Sheth
 تاريخ النشر 2008
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Ravi K. Sheth




اسأل ChatGPT حول البحث

Linear theory provides a reasonable description of the velocity correlations of biased tracers both perpendicular and parallel to the line of separation, provided one accounts for the fact that the measurement is almost always made using pair-weighted statistics. This introduces an additional term which, for sufficiently biased tracers, may be large. Previous work suggesting that linear theory was grossly in error for the components parallel to the line of separation ignored this term.

قيم البحث

اقرأ أيضاً

Because all stars contribute to its gravitational potential, stellar clusters amplify perturbations collectively. In the limit of small fluctuations, this is described through linear response theory, via the so-called response matrix. While the evalu ation of this matrix is somewhat straightforward for unstable modes (i.e. with a positive growth rate), it requires a careful analytic continuation for damped modes (i.e. with a negative growth rate). We present a generic method to perform such a calculation in spherically symmetric stellar clusters. When applied to an isotropic isochrone cluster, we recover the presence of a low-frequency weakly damped $ell = 1$ mode. We finally use a set of direct $N$-body simulations to test explicitly this prediction through the statistics of the correlated random walk undergone by a clusters density centre.
We investigate peculiar velocities predicted for clusters in Lambda cold dark matter ($Lambda$CDM) models assuming that the initial density fluctuation field is Gaussian. To study the non-linear regime, we use N-body simulations. We investigate the r ms velocity and the probability distribution function of cluster peculiar velocities for different cluster masses. To identify clusters in the simulation we use two methods: the standard friends-of-friends (FOF) method and the method, where the clusters are defined as maxima of a smoothed density field (DMAX). The density field is smoothed with a top-hat window, using the smoothing radii $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc. The peculiar velocity of the DMAX clusters is defined to be the mean peculiar velocity of matter within a sphere of the radius $R_s$. We find that the rms velocity of the FOF clusters decreases as the cluster mass increases. The rms velocity of the DMAX clusters is almost independent of the cluster mass and is well approximated by the linear rms peculiar velocity smoothed at the radius $R=R_s$. The velocity distribution function of the DMAX clusters is similar to a Gaussian.
We study a $2d$ Hamiltonian fluid made of particles carrying spins coupled to their velocities. At low temperatures and intermediate densities, this conservative system exhibits phase coexistence between a collectively moving droplet and a still gas. The particle displacements within the droplet have remarkably similar correlations to those of birds flocks. The center of mass behaves as an effective self-propelled particle, driven by the droplets total magnetization. The conservation of a generalized angular momentum leads to rigid rotations, opposite to the fluctuations of the magnetization orientation that, however small, are responsible for the shape and scaling of the correlations.
274 - Y. Malevergne 2001
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we give exact formulas for the ta ils and for the moments and cumulants of the distribution of returns of a portfolio make of arbitrary compositions of these assets. Using combinatorial and hypergeometric functions, we are in particular able to extend previous results to the case where the exponents of the Weibull distributions are different from asset to asset and in the presence of dependence between assets. We treat in details the problem of risk minimization using two different measures of risks (cumulants and value-at-risk) for a portfolio made of two assets and compare the theoretical predictions with direct empirical data. While good agreement is found, the remaining discrepancy between theory and data stems from the deviations from the Weibull parameterization for small returns. Our extended formulas enable us to determine analytically the conditions under which it is possible to ``have your cake and eat it too, i.e., to construct a portfolio with both larger return and smaller ``large risks.
In a classical online decision problem, a decision-maker who is trying to maximize her value inspects a sequence of arriving items to learn their values (drawn from known distributions), and decides when to stop the process by taking the current item . The goal is to prove a prophet inequality: that she can do approximately as well as a prophet with foreknowledge of all the values. In this work, we investigate this problem when the values are allowed to be correlated. Since non-trivial guarantees are impossible for arbitrary correlations, we consider a natural linear correlation structure introduced by Bateni et al. [ESA 2015] as a generalization of the common-base value model of Chawla et al. [GEB 2015]. A key challenge is that threshold-based algorithms, which are commonly used for prophet inequalities, no longer guarantee good performance for linear correlations. We relate this roadblock to another augmentations challenge that might be of independent interest: many existing prophet inequality algorithms are not robust to slight increase in the values of the arriving items. We leverage this intuition to prove bounds (matching up to constant factors) that decay gracefully with the amount of correlation of the arriving items. We extend these results to the case of selecting multiple items by designing a new $(1+o(1))$ approximation ratio algorithm that is robust to augmentations.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا