On Some Limit Properties For The Generalized Allocation Scheme

Random assignment(random occupancy)is one of the important models in probabil-ity and statistics,and it is of great theoretical significance to study its limit properties.The first part is concerned with the background of the subject,the significance and the main research content of this paper.And then the models studied in this paper are also introduced.The approach based on the generalized allocation scheme has received accep-tance in probabilistic combinatorics,and this approach reduces a number of combinatorial problems to problems on sums of independent random variables,the classical subject of investigation in probability theory.In the second chapter,we first introduce some relevant probability basics,such as law of large numbers,central limit theorem and moderate deviation principle.Then we introduce some symbols used in the process of proof.Finally,we give some lemmas which are needed to prove the main results of this paper.In the third chapter,we will give our main results and their proof.We consider the power series random variable which is often used in the framework to study the generalized allocation scheme,and establish some asymptotic properties which include law of large numbers,moderate deviation principle,almost sure central limit theorem and the rate of local limit theorem.And we also establish some limit behaviors for the generalized allocation scheme driven by m-dependent random variables.