204 citations · 636 across the 40 of their papers we have counts for
19 papers · 1 filter
Random walks on with metastable Gaussian distribution caused by linear drift with application to the contact process on the complete graph
O. S. Awolude, E. Cator, H. Don
We study random walks on which have a linear (or almost linear) drift towards 0 in a range around 0. This drift leads to a metastable Gaussian distribution centered at…
On the Geometry of the Last Passage Percolation Problem
Tom Alberts, Eric Cator
We analyze the geometrical structure of the passage times in the last passage percolation model. Viewing the passage time as a piecewise linear function of the weights we determine…
Attractiveness of Brownian queues in tandem
Eric A. Cator, Sergio I. Lopez, Leandro P. R. Pimentel
Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering in the first queue is a zero mean ergodic process. We prove…
Explicit bounds for critical infection rates and expected extinction times of the contact process on finite random graphs
Eric Cator, Henk Don
We introduce a method to prove metastability of the contact process on Erdős-Rényi graphs and on configuration model graphs. The method relies on uniformly bounding the total infec…
Self-averaging sequences which fail to converge
Eric Cator, Henk Don
We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a lim…
Conditioned multi-type Galton-Watson trees
Eric Cator, Henk Don
We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned…