Background and Professional Information
- Ph.D.in Mathematics, University of Illinois (Champaign-Urbana), 1979.
- M.S. in Statistics, University of Illinois (Champaign-Urbana), 1979.
- M.A. in Counseling Psychology, Regis University (Denver), 1998
- Associate Professor at Univ. Colorado Colorado Springs 1986-2006.
- Professor at Univ. Colorado Colorado Springs 2006-Present.
- Random Walk, Percolation
- Tai Chi
- Jungian and Process Oriented psychologies
“Bernoulli number identities for associated Stirling numbers and derangements”, preprint:
“Gambler’s ruin with random stopping”, revised preprint:
Probabilistic aspects of r-Stirling numbers:
Laws relating runs, long runs, and steps in gambler’s ruin, with persistence in two strata. Lattice Path Combinatorics and Applications, George E. Andrews, Christian Krattenthaler, Alan Krinik, eds., Springer Developments in Mathematics Vol. 58 (2019) 343-381.
Mathematica calculations for Laws relating runs, long runs, and steps in gambler’s ruin, with persistence in two strata, companion document:
Laws relating runs and steps in gambler’s ruin, Stoch. Proc. Appl.125 (2015) 2010-2025.
Time constant for the once oriented last passage percolation in high dimensions, Dependence in Probability, Analysis, and Number Theory, I. Berkes, R. C. Bradley, H. Dehling, M. Peligrad and R. Tichy, eds., Kendrick Press (2010).
(with Y. Zhang) The sizes of the pioneering, lowest crossing, and pivotal sites in critical percolation on the triangular lattice,Ann. Appl. Probab. 15, 1832-1886 (2005).
(with S. Chakravarty) Statistical Analysis of collision-induced timing shifts in a wavelength-division-multiplexed optical soliton-transmission system, Contemporary Mathematics301, 235-247 (2002).
(with R. Schinazi and Y. Zhang) The critical contact process on a homogeneous tree, J. Appl. Prob., 31, 250-255, (1994).
Large deviation results for a class of Markov chains with applications to an infinite alleles model of population genetics, Ann. Appl. Probab., 2, 857-905 (1992).
(with S. Sawyer) Large deviation results for a class of Markov chains arising from population genetics, Ann. Probab. 17, 1124-1146 (1989).
Central limit theorem for linearly dependent fields of continuous elements, Prob. Th. Rel. Fields, 75, 87-95 (1987).
University of Denver Analysis Seminar, 2016: (Slides) Large deviations for certain integer valued statistics in gambler’s ruin.
8th International Conference on Lattice Path Combinatorics & Applications, Cal Poly Pomona, 2015: (Slides) Laws relating runs, long runs, and steps in gambler’s ruin, with persistence in two strata.
Frontier Probability Days 2014, Tucson: (Slides) Laws relating runs and steps in gambler’s ruin.
Conference in Memory of Walter V. Philipp, June, 2009: Talk on an asymptotic evaluation of the last passage time constant in high dimensions.
(with B. Rider and O. Poliannikov) Frontier Probability Days 2007 Conference at CU-Colorado Springs: FPD07 Program