Paul C. Shields

A diffusion limit for a class of randomly-growing binary trees

SummaryBinary trees are grown by adding one node at a time, an available node at height i being added with probability proportional to c-i, c>1. We establish both a “strong law of large numbers” and a “central limit theorem” for the vector X(t)=(Xi(t)), where Xi(t) is the proportion of nodes of height i that are available at time t. We show, in fact, that there is a deterministic process xi(t) such that

Redundancy rates for renewal and other processes

\sum {|X_i (t) - x_i (t)|} {\text{ converges to 0 a}}{\text{.s}}{\text{.,}}

Cutting and stacking: a method for constructing stationary processes

and such that if c2

Block and sliding-block source coding

\tfrac{1}{2}

The ergodic and entropy theorems revisited

,