I am a faculty member (now retired) with the Mathematics Department of the University of North Carolina at Chapel Hill

Degrees: AB 1965

Specialty: Ergodic theory

Ergodic theory is a fairly new branch of mathematics which applies
probability and analysis to study the long-term average behavior of complicated
systems. It overlaps heavily with (smooth) dynamical systems theory and draws
methods, examples, and problems from harmonic analysis, number theory,
combinatorics, and many other branches of mathematics. Applications range from
celestial mechanics through interactions of biological populations to the
efficient transmission and recording of information. My particular research
interests have concentrated on symbolic dynamics, almost everywhere
convergence, maximal theorems, and connections of ergodic theory with harmonic
analysis and probability.

Mathematics 56H, First-Year Seminar, Information and Coding

T-Th 11:00-12:15, Phillips 228

Notes on Elementary Probability

Notes on Number Theory and Cryptography

Notes on Shannon's Information Theory

Symbolic Dynamics--Math. 261, Spring 1998

Attractors and Attracting Measures--Math. 261, Spring 1997

Notes on dynamics of continued fractions from Spring 2000 Math. 261:

Notes of lecture course at Workshop on Dynamics and
Randomness,

Short courses on ergodic theory in

Sofic Measures: Characterizations of hidden Markov chains by linear alebra, formal languages, and symbolic dynamics--Math. 210, Spring 2006

Measure-Preserving Systems--Math. 857, Spring 2007

Measuring Complexity in Cantor Dynamics---Lectures at the CIMPA Research School 2--13 November 2015

Recent Talks

Some Sturmian Symbolic Dynamics. Queen Mary University of London, June 22, 2009.

Adic Systems and Symbolic Dynamics. Short Course at Pingree Park, Colorado, July 2014.

Recent reprints and preprints:

*Random ergodic theorems with universally
representative sequences* (with Michael Lacey, Dan Rudolph, and Mate Wierdl)

Ann. Inst. H. Poincaré 30 (1994),
353-395.

The form here is an earlier version, produced by Exp to

univ.dvi

univ.pdf

*Ergodic theorems and the basis of science*

Synthese 108 (1996), 171-183.

phil.dvi

phil.pdf

*Symmetric Gibbs measures* (with Klaus Schmidt)

Trans. Amer. Math. Soc. 349 (1997), 2775-2811.

gibbs6.dvi

gibbs6.pdf

*Binomial-coefficient multiples of irrationals*
(with Terrence M. Adams)

Monatsh. f. Math. 125 (1998), 269-278.

adams8.dvi

adams8.pdf

*Factor maps between tiling dynamical systems*

Forum Math. 11 (1999), 503-512.

tilecode.dvi

tilecode.pdf

*Nearly simultaneous proofs of the Ergodic Theorem
and Maximal Ergodic Theorem*

(with Michael Keane)

KeanePetersenLNMS.dvi

KeanePetersenLNMS.pdf

KeanePetersenLNMS.ps

*Measures of maximal relative entropy* (with
Anthony Quas and Sujin Shin)

Erg. Th. Dyn. Sys. 23 (2003), 207-223.

pqsfinal.pdf

*Tail fields generated by symbol counts in measure-preserving systems*
(with Jean-Paul Thouvenot)

Colloq. Math. 101 (2004), 9-23.

quant10.dvi

quant10.ps

quant10.pdf

*Dynamical properties of the Pascal adic
transformation* (with Xavier Méla)

Erg. Th. Dyn. Sys. 25 (2005), 227-256.

part1.pdf

*On the definition of relative pressure for factor maps
on shifts of finite type *(with Sujin Shin)

Bull.

RPfinal.ps

RPfinal.pdf

*Ergodicity of the adic transformation on the Euler
graph* (with Sarah Bailey, Michael Keane, and Ibrahim Salama), Math. Proc. Camb. Phil. Soc. 141 (2006), 231-238.

EulerErgodicity.pdf

*Random permutations and unique fully supported
ergodicity for the Euler adic transformation* (with Sarah Bailey Frick),
Ann. Inst. Henri Poincare Prob. Stat. 44 (2008), 876-885.

AIHP133.pdf

*Measure-Preserving Systems*,
Springer Online Encyclopedia of Complexity

*Basic Constructions and Examples* (with Matthew Nicol), Springer Online Encyclopedia of Complexity

*Reinforced random walks and adic transformations*
(with Sarah Bailey Frick),
J. Theoret. Probab. 23 (2010), no. 3, 920-943.

*The Euler adic dynamical system and path counts in the Euler graph*
(with Alexander Varchenko), Tokyo J. Math. 33, No. 2 (2010), 327-340.

*Path count asymptotics and Stirling numbers*
(with Alexander Varchenko), Proc. Amer. Math. Soc. 140 (2012), 1909-1919.

*Hidden Markov processes in the context of symbolic dynamics*
(with Mike Boyle), in
*Entropy of Hidden Markov Processes and Connections to Dynamical Systems*,
London Math. Soc. Lecture Note Ser., 385, Cambridge Univ. Press, Cambridge, 2011, 5-71.

*An adic dynamical system related to the Delannoy numbers*, Erg. Th. Dyn. Sys. 32 (2012), 809-823.

*Markov diagrams for some non-Markovian systems* (with Kathleen Carroll), Contemp. Math. 678 (2016), 73-101.

*Dynamical properties of some adic systems with arbitrary orderings* (with Sarah Frick and Sandi Shields), Erg. Th. Dyn. Sys. 2016.

*Dynamical intricacy and average sample complexity* (with Benjamin Wilson), Dynamical Systems, http://dx.doi.org/10.1080/14689367.2017.1374352, 2017.

*Constructive symbolic presentations of rank one measure-preserving systems* (with Terrence Adams and Sébastien Ferenczi), Colloq. Math. 150 (2017), 243-255.

*Tree shift complexity* (with Ibrahim Salama), 2017.

Books:

*Brownian Motion, Hardy Spaces and Bounded Mean
Oscillation *, LMS Lecture Note Series 28, 1977.

*Ergodic Theory*, 1983; corrected paperback
edition, 1989. Errata.

*Ergodic Theory and Its Connections with Harmonic
Analysis: Proceedings of the 1993 *with Ibrahim A. Salama, LMS Lecture Note Series 205, 1995.

*Entropy of Hidden Markov Processes and Connections to Dynamical Systems:
Papers from the Banff International Research Station Workshop, *with Brian Marcus and Tsachy Weissman,
LMS Lecture Note Series 385, 2011.

These are available from Cambridge University Press,

Courseware:

*Calculus Explorer and Tutor I and II *, 11
diskettes plus Student Guide, 1994.

HarperCollinsCollegePublishers,