Random matrices with complex Gaussian entries

In this paper we give new and purely analytical proofs of a number of classical results on the asymptotic behavior of large random matrices of complex Wigner type (the GUE-case) or of complex Wishart type: Wigner's semi-circle law, the Harer-Zagier recursion formula, the Marchenko-Pastur law, the Geman-Silverstein results on the largest and smallest eigenvalues and other related results. Our approach is based on the derivation of explicit formulae for the moment generating functions for random matrices of the two considered types.     

Asymptotics on Two-dimensional Recursion Sequences

In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.     

Separation of unitary representations of connected Lie groups by their moment sets

We show that every unitary representation π of a connected Lie group G is characterized up to quasi-equivalence by its complete moment set.Moreover, irreducible unitary representations π of G are characterized by their moment sets.     

同分布两两NQD列的最大值不等式及其应用

设{xn，n≥1}是同分布的两两NQD列，记Sn=∑i=1Xi^n．本文讨论了max ｜Si｜/i（n≥1）的分布函数的上下界．作为应用，获得了随机变量supn≥｜Sn｜/n型的1阶矩及p（〉1）阶矩分别存在有限的充分必要条件，这是一个与独立同分布场合相一致的结果．     

Connections between Romanovski and other polynomials

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.     

Replenishment-Depletion Urn in Equilibrium

An urn has balls of colors C1 and C2. It is replenished (R) by balls of both colors and then depleted by (D) the same number; this constitutes a cycle. When R = D, the system is closed and equilibrium will be reached after many cycles. The ultimate distribution is found only when the replenishment is the same for each color. Asymptotic normal and asymptotic binomial distributions arise when the parameters reach extreme values. For the multicolor urn an expression is given for the correlation between the number of balls of any two colors.     

Exponential Transformation in Convexifying a Noninferior Frontier and Exponential Generating Method

The convexification of a noninferior frontier can be achieved in an appropriate equivalent objective space for general nonconvex multiobjective optimization problems. Specifically, this paper proves that taking the exponentials of the objective functions can act as a convexification scheme. This convexification scheme further leads to the exponential generating method that guarantees the identification of the entire set of noninferior solutions.     

Analysis of an retrial queue

We consider a single server retrial queueing system in which each customer (primary or retrial customer) has discrete service times taking on value D_j with probability , and . An arriving primary customer who finds the server busy tries later. Moreover, each retrial customer has its own orbit, and the retrial customers try to enter the service independently of each other. We call this retrial queue an M/{D_n}/1 retrial queue. A necessary and sufficient condition for this system stability is given. In the steady state, we derive the joint distribution of the state of the server and the number of customers in the retrial orbits. The explicit expressions of some performance measures are given. In addition, the steady-state distribution of the waiting time is discussed.     

Single line queue with repeated demands

We analyze a model of a queueing system in which customers can only call in to request service: if the server is free, the customer enters service immediately, but if the service system is occupied, the unsatisfied customer must break contact and reinitiate his request later. Such a customer is said to be in “orbit”. In this paper we consider three models characterized by the discipline governing the order of re-request of service from orbit. First, all customers in orbit can reapply, but are discouraged and reduce their rate of demand as more customers join the orbit. Secondly, the FCFS discipline operates for the unsatisfied customers in orbit. Finally, the LCFS discipline governs the customers in orbit and the server takes an exponentially distributed vacation after each service is completed. We calculate several characteristics quantities of such systems, assuming a general service-time distribution and different exponential distributions for the times between arrivals of first and repeat requests.