The distributions of vertex degrees in random recursive trees and random plane recursive trees are shown to be asymptotically normal. Formulas are given for the asymptotic variances and covariances of the number of vertices with given outdegrees. We also give functional limit theorems for the evolution as vertices are added. The proofs use some old and new results about generalized Pólya urn mo...

The behavior of one-dimensional quantum random walks is strikingly different from that of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we study the decoherence on both position and “coin” spaces of the particle. We propose an analytical approach to investigate these phenomena and obtain the generating...

In the previous century, much work has been done on the spectra of random matrices. However, not much is known about the spectra of matrices formed from pseudo-random sequences. In this talk, I will discuss some of our recent results (jointly with Behtash Babadi) in this direction. First, we consider a binary linear block code C of length N , dimension k and minimum Hamming distance d over GF(2...

Abstract: Let X,Y,B be three independent random variables such that X has the same distribution function as Y B. Assume that B is a Beta random variable with positive parameters α, β and Y has distribution function H with H(0) = 0. Pakes and Navarro (2007) show under some mild conditions that the distribution function Hα,β of X determines H . Based on that result we derive in this paper a recur...

We present a technique for automatically deriving test data generators from a predicate expressed as a Boolean function. The distribution of these generators is uniform over values of a given size. To make the generation efficient we rely on laziness of the predicate, allowing us to prune the space of values quickly. In contrast, implementing test data generators by hand is labour intensive and...

We consider ensembles of random polynomials of the form p(z) = ∑N j=1 ajPj where {aj} are independent complex normal random variables and where {Pj} are the orthonormal polynomials on the boundary of a bounded simply connected analytic plane domain Ω ⊂ C relative to an analytic weight ρ(z)|dz| . In the simplest case where Ω is the unit disk and ρ = 1, so that Pj(z) = z j , it is known that the ...