The present work studies some aspects of random matrix theory. Its first part is devoted to the asymptotics of random matrices with infinitely divisible, in particular heavy-tailed, entries. Its second part focuses on relations between limiting law in subsequence problems and spectra of random matrices.

The primary purpose of this work is to study, implement and analyze the performance of parallel algorithms related to subsequence problems. The problems include string to string correction problem, to determine the longest common subsequence problem and solving the sum-range-product, 1 —D pattern matching, longest non-decreasing (non-increasing) (LNS) and maximum positive subsequence (MPS) problems. The work also includes studying the techniques and issues involved in developing parallel applications. These algorithms are implemented on the Sequent Multiprocessor System. The subsequence problems have been defined, along with performance metrics that are utilized. The sequential and parallel algorithms have been summarized. The implementation issues which arise in the process of developing parallel applications have been identified and studied.