Probability and deterministic problems of minimal interval

A problem of a minimal interval between neighbor points appears in different applications: in the solid state physics, in the surface physics, in the mathematical economics, in the operations research and etc. From a mathematical point of view these problems are sufficiently substandard and demand a creation of special approaches. In this paper as probability so deterministic formulations of this problem are considered. Original algorithms of the problem solution and asymptotic formulas are constructed.