Stewart Ethier, Professor Emeritus (retired in 2016)

Department of Mathematics, University of Utah, 155 S. 1400 E., JWB 233, Salt Lake City, UT 84112, USA.
ethier@math.utah.edu.
801-581-6851 (dept. office, JWB 233), 801-581-4148 (dept. fax).

Papers since 2009 (arXived):

Parrondo's paradox:

Limit theorems for Parrondo's paradox with Jiyeon Lee. Electronic Journal of Probability 14 (2009) 1827-1862.
A Markovian slot machine and Parrondo's paradox with Jiyeon Lee. Annals of Applied Probability 20 (2010) 1098-1125.
A discrete dynamical system for the greedy strategy at collective Parrondo games with Jiyeon Lee. Dynamical Systems 26 (2011) 401-424.
Parrondo's paradox via redistribution of wealth with Jiyeon Lee. Electronic Journal of Probability 17 (2012) (20) 1-21.
Parrondo games with spatial dependence with Jiyeon Lee. Fluctuation and Noise Letters 11 (2012) (1250004) 1-22.
Parrondo games with spatial dependence, II with Jiyeon Lee. Fluctuation and Noise Letters 11 (2012) (1250030) 1-18.
Parrondo games with spatial dependence and a related spin system with Jiyeon Lee. Markov Processes and Related Fields 19 (2013) 163-194.
Parrondo games with spatial dependence and a related spin system, II with Jiyeon Lee. Markov Processes and Related Fields 19 (2013) 667-692.
Parrondo games with spatial dependence, III with Jiyeon Lee. Fluctuation and Noise Letters 14 (2015) (1550039) 1-20.
Parrondo games with two-dimensional spatial dependence with Jiyeon Lee. Fluctuation and Noise Letters 16 (2017) (1750005) 1-23.
The flashing Brownian ratchet and Parrondo's paradox with Jiyeon Lee. Royal Society Open Science 5 (2018) (171685) 1-13.
The tilted flashing Brownian ratchet with Jiyeon Lee. Fluctuation and Noise Letters 18 (2019) (1950005) 1-19.
How strong can the Parrondo effect be? with Jiyeon Lee. Journal of Applied Probability 56 (2019) 1198-1216.
How strong can the Parrondo effect be? II with Jiyeon Lee. Contemporary Mathematics, an AMS volume honoring M. M. Rao, to appear.

Gambling/game theory:

A world record in Atlantic City and the length of the shooter's hand at craps with Fred M. Hoppe. Mathematical Intelligencer 32 (2010) (4) 44-48.
A game-theoretic analysis of baccara chemin de fer with Carlos Gamez. Games 4 (2013) 711-737.
On the three-person game baccara banque with Jiyeon Lee. Games 6 (2015) 57-78.
The evolution of the game of baccarat with Jiyeon Lee. Journal of Gambling Business and Economics 9 (2015) (2) 1-13.
Optimal conditional expectation at the video poker game Jacks or Better with John Jungtae Kim and Jiyeon Lee. UNLV Gaming Research & Review Journal 23 (2019) 1-18.
Teaching a university course on the mathematics of gambling with Fred M. Hoppe. UNLV Gaming Research & Review Journal 24 (2020) 1-35.
Snackjack: A toy model of blackjack with Jiyeon Lee. UNLV Gaming Research & Review Journal 24 (2020) 49-82.
Gambler's ruin and the ICM with Persi Diaconis. Statistical Science, to appear.
A note on Bertrand's analysis of baccarat.

Diffusion processes/population genetics:

A property of Petrov's diffusion. Electronic Communications in Probability 19 (2014) (65) 1-4.
Wright-Fisher construction of the two-parameter Poisson-Dirichlet diffusion with C. Costantini, P. De Blasi, M. Ruggiero, D. Spano. Annals of Appl. Probab. 27 (2017) 1923-1950.

Combinatorics:

Counting toroidal binary arrays. Journal of Integer Sequences 16 (2013) (13.4.7) 1-8.
Counting toroidal binary arrays, II with Jiyeon Lee. Journal of Integer Sequences 18 (2015) (15.8.3) 1-12.

Books:

Markov Processes: Characterization and Convergence with Thomas G. Kurtz (paperback edition), 2005. Wiley.
Optimal Play: Mathematical Studies of Games and Gambling (edited with William R. Eadington), 2007. Institute for the Study of Gambling and Commercial Gaming.
Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz (edited with Jin Feng and Richard H. Stockbridge), 2008. Institute of Mathematical Statistics.
The Doctrine of Chances: Probabilistic Aspects of Gambling, 2010. Springer.

CV: Download here. Updated Jan. 2020.

An incomplete list of my mathematical ancestors (see Mathematics Genealogy Project for the full list):

T. G. Kurtz, J. L. McGregor, H. F. Bohnenblust, E. C. Hille, M. Riesz, L. Fejer, H. A. Schwarz, E. E. Kummer and K. T. W. Weierstrass, H. F. Scherk, F. W. Bessel and H. W. Brandes, C. F. Gauss.

Personal: My dog, Cauchy (2003--2016), trying to comprehend Cauchy's theorem in complex analysis. (Photo motivated by Far Side cartoon.) Cauchy was a Cavalier King Charles Spaniel.