Inequalities in Probability Theory and Turán-Type Problems for Graphs with Colored Vertices

Abstract

The “best” inequalities of type P{(ζ, η)⊂ E} ≧f(P{η⊂ D1}P{η⊂Dm}) for independent and identically distributed random elements ζ and η can be reduced to Turan-type problems for graphs with colored vertices. In the present work we describe a finite algorithm for obtaining the asymptotical solution for an arbitrary problem of such type. In the case of two colors we obtain the final form of asymptotic solution without using the algorithm.