In this paper, we consider a random entire function of the form f(z,?)=?n=0+??n(?1)×?n(?2)fnzn, where (?n) is sequence independent Steinhaus variables, (?n) standard complex Gaussian and numbers fn?C such that lim¯n?+?|fn|n=0 #{n:fn?0}=+?. We investigate asymptotic estimates probability P0(r)=P{?:f(z,?) has no zeros inside rD} as r?+? outside some set E finite logarithmic measure, i.e., ?E?[1,+...

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) real-space density, redshift-space and their geometric mean. We find that density PDF is well-described by function two parameters: $n_s$, spectral slope, $\sigma_L$, linear rms fluctuation. For mean real- densities, introduce third parameter, $s_L={\sqrt{\langle(dv^L_{\rm pec}/dr)^2...

Abstract We investigated the probability distributions of sunspot area and magnetic flux by using data from Royal Greenwich Observatory USAF/NOAA. constructed a sample 2995 regions with maximum-development areas ≥500 MSH (millionths solar hemisphere), covering 146.7 yr (1874–2020). The were fitted power-law distribution four two-parameter (tapered-power-law, gamma, lognormal, Weibull distributi...