Two goals of this proposal are to extend some known results for the uniform random mapping model to other interesting random mapping models, and to initiate new research on probabilistic optimization problems. The work on random mapping models is a continuation of work already completed by the principal investigator. In particular, the principal investigator is interested in determining new central limit theorems and functional limit theorem for certain random mapping models. The investigation of probabilistic optimization problems is related to the study of random mapping models, as both rely, in various ways, on the theory of random graphs. Since the second topic of this proposal is a new area of research for the investigator, the planning activities that will be carried out are primarily intended to prepare the proposer to work independently in this field.
