Related papers: The relationship between extremum statistics and u…
A probabilistic description is essential for understanding growth processes far from equilibrium. In this paper, we compute time-dependent Probability Density Functions (PDFs) in order to investigate stochastic logistic and Gompertz models,…
We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
One of the principle efforts in cosmic microwave background (CMB) research is measurement of the parameter fnl that quantifies the departure from Gaussianity in a large class of non-minimal inflationary (and other) models. Estimators for…
The eigenvalue probability density function (PDF) for the Gaussian unitary ensemble has a well known analogy with the Boltzmann factor for a classical log-gas with pair potential $- \log | x - y|$, confined by a one-body harmonic potential.…
This paper covers the material of our two talks. We describe a series of projects based upon perturbative expansions to follow the gravitational evolution of the one point probability distribution functions (PDFs) for the density contrast…
We study the interface representation of the contact process (CP) at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a…
One of the most puzzling properties of observed galaxies is the universality of the empirical correlation between the star formation rate and average gas surface density on kiloparsec scales (the Schmidt law). In this study I present…
We report on probability-density-functions (PDF) of the mass density in numerical simulations of highly compressible hydrodynamic flows and the corresponding structure formation of Lagrangian particles advected by the flows. Numerical…
We describe the statistical properties of two large river systems: the Danube and the Mississippi. The properties of the two rivers are compared qualitatively to the general properties of a critical steady state system. Specifically, we…
At large values of $x$ the parton distribution functions (PDFs) of the proton are poorly constrained and there are considerable variations between different global fits. Data at such high $x$ have already been published by the ZEUS…
Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of…
We study the correlation between different sets of parton distributions (PDFs). Specifically, viewing different PDF sets as distinct determinations, generally correlated, of the same underlying physical quantity, we examine the extent to…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
Time series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various timescales,…
We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme…
This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density…
Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical…
We show that density fluctuations in standard inflationary scenarios may take the most general non-Gaussian distribution if the wave function of the Universe is not in the ground state. We adopt the Schr\"odinger picture to find a…