J. T. Campbell

activity

20122021

collaborators

4 papers

math.PR2021

The Lightning Model

James Campbell, Alexandra Deane, Anthony Quas

We introduce a non-standard model for percolation on the integer lattice $Z^{2}$ . Randomly assign to each vertex $a \in Z^{2}$ a potential, denoted $ϕ_{a}$ , chosen indepe…

math.DS2018

Independence and Alpern Multitowers

James T. Campbell, Randall McCutcheon, Alistair Windsor

Let $T$ be any invertible, ergodic, aperiodic measure-preserving transformation of a Lebesgue probability space $(X, \calB, μ)$, and ¶\, any finite measurable partition of $X$ . We…

math.DS2018

An Alpern tower independent of a given partition

J. T. Campbell, J. T. Collins, R. King +2

Given a measure-preserving transformation $T$ of a probability space $(X, B, μ)$ and a finite measurable partition $P$ of $X$ , we show how to construct an Alpern tower of…

math.DS2012

Specifying attracting cycles for Newton maps of polynomials

James T. Campbell, Jared T. Collins

We show that for any set of n distinct points in the complex plane, there exists a polynomial p of degree at most n+1 so that the corresponding Newton map, or even the relaxed Newt…