Limiting distributions of two random sequences

Hildenbrand Distribution Economies as Limiting Empirical Distributions of Random Economies ∗

The present note shows that the concept of a distribution economy (Hildenbrand (1974)) is closely related to a framework of an exchange economy in which the agents’ individual characteristics (i.e. preferences and endowments) are random (Hildenbrand (1971), Bhattacharya and Majumdar (1973), Föllmer (1974)). A random exchange economy is fully specified by the distribution of the family of random...

Limiting Distributions for Sums of Independent Random Products

Let {Xi,j : (i, j) ∈ N } be a two-dimensional array of independent copies of a random variable X, and let {Nn}n∈N be a sequence of natural numbers such that limn→∞ e Nn = 1 for some c > 0. Our main object of interest is the sum of independent random products

Sturm Sequences and Random Eigenvalue Distributions

This paper proposes that the study of Sturm sequences is invaluable in the numerical computation and theoretical derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric tridiagonal matrices and apply these ideas to random matrix ensembles such as the β-Hermite ensemble. Using ou...

General Tridiagonal Random Matrix Models, Limiting Distributions and Fluctuations

In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given in [3] and [4]. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions in some particular cases. We also discuss the limit of fluctuations, which, in a general context, turn out to be Gaussian. For the case of several random matrices, we ...

SOME LIMITING DISTRIBUTIONS RELATED TO THE SUM OF A RANDOM NUMBER OF RANDOM VARIABLES1 edward paulson