Molecular clouds have power-law probability distribution functions

Column Density Probability Distribution Functions in Turbulent Molecular Clouds: A Comparison between Theory and Observations

The one-point statistics of column density distributions of turbulent molecular cloud models are investigated and compared with observations. In agreement with the observations, the number N of pixels with surface density Σ is distributed exponentially N(Σ) ∼ exp(−Σ/Σ0) in models of driven compressible supersonic turbulence. However, in contrast to the observations, the exponential slope define...

Inferring Trading Strategies from Probability Distribution Functions Inferring Trading Strategies from Probability Distribution Functions

On the Concavity of Multivariate Probability Distribution Functions on the Concavity of Multivariate Probability Distribution Functions

We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems.

On the scaling of probability density functions with apparent power-law exponents less than unity

We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent τ̃ of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling exponent τ equal to 1, provided that the fraction of events in the universal scaling part of the probability density function is non-vanishing in the thermodynamic limi...

Nonuniversal power law scaling in the probability distribution of scientific citations

We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find...