Consider a situation in which balls are falling into N cells with arbitrary probabilities. A limiting distribution for the number of occupied cells after n falls is obtained, when n and N → ∞, so that ...

Using the central limit theorem concerning the distribution of means allows one to justify the assumption of the normal distribution. Analytical people tend not to worry too much about the nature of ...

A reduction theorem is proved for functionals of Gamma-correlated random fields with long-range dependence in d-dimensional space. As a particular case, integrals of non-linear functions of ...

Random fields provide a versatile mathematical framework to describe spatially dependent phenomena, ranging from physical systems and quantum chaos to cosmology and spatial statistics. Underpinning ...

Random walks constitute one of the cornerstone concepts in probability theory and statistical physics, representing a class of stochastic processes in which a moving entity takes successive steps in ...