Related papers: Common probability patterns arise from simple inva…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
A change in a stochastic system has three representations: Probabilistic, statistical, and informational: (i) is based on random variable $u(\omega)\to\tilde{u}(\omega)$; this induces (ii) the probability distributions $F_u(x)\to…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
The state of a stochastic process evolving over a time $t$ is typically assumed to lie on a normal distribution whose width scales like $t^{1/2}$. However, processes where the probability distribution is not normal and the scaling exponent…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…
We consider transition to strong turbulence in an infinite fluid stirred by a gaussian random force. The transition is {\bf defined} as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
We consider the classical dynamics of bosonic and fermionic matrix variables in complex Hilbert space, defined by a trace action, assuming cyclic invariance under the trace and the presence of a global unitary invariance. With plausible and…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
For rotationally invariant first passage percolation (FPP) on the plane, we use a multi-scale argument to prove stretched exponential concentration of the first passage times at the scale of the standard deviation. Our results are proved…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…
Telescoping sums very naturally lead to probability distributions on ${\mathbb Z}^+$. But are these distributions typically cosmetic and devoid of motivation? In this paper we give three examples of "first occurrence" distributions, each…
By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole to dynamical relations describing the evolution of…
Constructions in type-driven compositional distributional semantics associate large collections of matrices of size $D$ to linguistic corpora. We develop the proposal of analysing the statistical characteristics of this data in the…
We study the scaling behaviors in the wind velocity time series collected at the atmospheric surface layer and compare them with two commonly used cascade models, the truncated stable distribution and the log-normal model. Results show that…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…