On partitions, surjections, and Stirling numbers

A Functional Approach to the Stationary Waiting Time and Idle Period Distributions of the GI/G/1 Queue

The GI/G/1 queueing model is regarded as a functional which maps the service and interarrival time distributions onto output quantities of interest, such as the stationary waiting time distribution. For the case where the input distributions have densities, techniques from infinite-dimensional analysis are used to obtain derivatives and Taylor...

Density and uniqueness in percolation

Tail Triviality for Sums of Stationary Random Variables

We study tail $\sigma$-fields and loss of memory associated with sums of stationary integer-valued random variables. An application concerns convergence in distribution of interarrival times in zero-one sequences.

On the Uniqueness of the Infinite Occupied Cluster in Dependent Two- Dimensional Site Percolation

We consider dependent site percolation on the two-dimensional square lattice, the underlying probability measure being invariant and ergodic under each of the translations and invariant under axis reflections. If this measure satisfies the FKG condition and if percolation occurs, then we show that the infinite occupied cluster is unique with...

An Algebraic Construction of a Class of One-Dependent Processes

A special class of stationary one-dependent two-valued stochastic processes is defined. We associate to each member of this class two parameter values, whereby different members receive different parameter values. For any given values of the parameters, we show how to determine whether: 1. a process exists having the given parameter values, and...

On the uniqueness of the infinite cluster in the percolation model

We simplify the recent proof by Aizenman, Kesten and Newman of the uniqueness of the infinite open cluster in the percolation model. Our new proof is more suitable for generalization in the direction of percolation-type processes with dependent site variables.

One-dimensional dynamics: The Schwarzian derivative and beyond

Most of the important results in the study of the dynamics of smooth interval maps ƒ : [0,1] —• [0,1] assume the condition that S f < 0 where S f is the Schwarzian derivative of ƒ.