Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local dens...

We calculate the exact formation probability of primordial black holes generated during collapse at horizon re-entry large fluctuations produced inflation, such as those ascribed to a period ultra-slow-roll. show that it interpolates between Gaussian small values average density contrast and Cauchy distribution values. The corresponding abundance may be larger than one by several orders magnitu...

In this article, we have introduced a new probability distribution having three parameters using half Cauchy family of named extended exponential distribution. The statistical properties and characteristics the proposed like hazard rate function (HRF), cumulative function, density (PDF), (CDF), quantile skewness, kurtosis are provided. estimated Cramer-Von-Mises (CVM) least-square estimation (L...

We show the existence of global weak solutions to a general class of kinetic models of homogeneous incompressible dilute polymers. The main new feature of the model is the presence of a general implicit constitutive equation relating the viscous part Sv of the Cauchy stress and the symmetric part D of the velocity gradient. We consider implicit relations that generate maximal monotone (possibly...

in this paper, we show that the chapman-kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a markov bilinear model. the stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.