Research & Publications

Preprints and Publications 

Most of my recent preprints are on my ArXiv page.

Link on title is to the journal publication.

* = undergradaute collaborator.

  1. (with Rinaldo Schinazi) Self-similarity in an exchangeable site-dynamics model. arxiv:2101.00705
  2. (with Mason DiCicco) Greedy Coupling of 3-State Markov Chains. PDF
  3. (with SangJoon Lee) Quasi-Limiting Behavior of Drifted Brownian Motion. Submitted.  arxiv:2001.04523
  4. (with Hugo Panzo, Philip Speegle* and R. Oliver Vanderberg*) Quasistationary Distributions for the  Voter Model on Complete Bipartite Graphs. Submitted.  arxiv:2004.10187
  5. (with Jonah Green*, Taylor Meredith*, Hugo Panzo* and Xioran Tan*) Finite-Memory Elephant Random Walk and the Central Limit Theorem for Additive Functionals. Accepted to Brazilian Journal of Probability. arxiv:1911.05716
  6. (with Carter Bedsole* and Grace O’Neil*). Power-Law Tails in a Fitness-Driven Model for Biological Evolution. Submitted.  arxiv:2001.00960
  7. (with Behrang Forghani) On Transformations of Markov Chains and Poisson Boundary. Trans. Amer. Math. Soc.373 (2020), 2207–2227.  arxiv:1909.11217
  8. (with Alexander Roitershtein and Rinaldo Schinazi)  A Random Walk with Catastrophes, Elec. J. of Probability 24 (2019), no. 28, 1–21. arxiv:1709:04780
  9. (with Roger Silva) On a Local Version of the Bak-Sneppen Model,  Journal of Statistical Physics, Vol. 173 (2) (2018), 362–380. arxiv:1609.04420
  10. (with Hugo Panzo) On the Subcritical Phase for a Homopolymer Model. Communications on Stochastic Analysis,Vol. 11 (2017), No. 4, 425–456. arxiv:1803.09335
  11. (with Rinaldo Schinazi)  A Stochastic Model for the Evolution of a Quasispecies , Journal of Statistical Physics, 162(2), 415–425. PDF
  12. (with Steven Miller) A Probabilistic Approach to Generalized Zeckendorf Decompositions . SIAM J. Discrete Math, Vol. 30 (2016), No. 2, 1302–1332. arxiv:1405.2379
  13. (with Hugo Panzo, and Elizabeth Tripp*) Efficient Coupling for Random Walk with Redistribution.  arxiv:1410.8234
  14. On Independence and Determination of Probability Measures,  Journal of Theoretical Probability Vol. 28(3), 968–975. PDF
  15. Coupling for Drifted Brownian Motion on an Interval with Redistribution from the Boundary,  Electronic Communications in Probability Vol. 19 (2014), no. 16, 1–11. PDF
  16. (with Diana Hay and Alexander Roitershtein) On Wallis-type products and Polya’s urn schemes,  American Mathematical Monthly Vol. 121, No. 5, 422–432. PDF
  17. (with Keith Conrad) Maclaurin’s Inequality and a Generalized Bernoulli Inequality ,   Mathematics Magazine Vol. 87, No. 1, 14–24. PDF
  18. An Empirical Process Interpretation of a Model of Species Survival, Stochastic Process.  Appl. 123 (2013), 475–489. PDF
  19. Principal Eigenvalue for Brownian Motion on a Bounded Interval with Degenerate Instantaneous Jumps,  Electronic Journal of Probability, Vol. 17 (2012), no. 87, 1–13. PDF
  20.  (with Michael Neumann)  Probabilistic Approach to Perron Root, the Group Inverse, and Applications ,  Linear and Multilinear Algebra, Vol. 60 (2012), no. 1,  39–63. PDF
  21. (with Michael Neumann and Olga Pryporova) Inequalities for Functions of Transition Matrices,  Linear Algebra and its Applications, Vol. 436 (2012), no. 2, 335–348. PDF
  22. (with Anastasios Matzavinos and Alexander Roitershtein) On a species survival model , Electronic Communications in Probability, Vol. 16 (2011) paper 22, 226–233. PDF
  23. (with Khalid Boushaba, Anastasios Matzavinos and Alexander Roitershtein) Stochastic Analysis of the Motion of DNA Nanomechanical Bipeds.  Bulletin of Mathematical Biology 73 (2011), no. 8, 1931–1951.  PDF
  24. (with Mathieu Merle and Alexander Roitershtein)  A random walk on Z with drift driven by its occupation time at zero .  Stochastic Process. Appl. 119 (2009), no. 8, 2682–2710. PDF
  25. Large Deviations For Partition Functions of Directed Polymers in an IID Field. Annales de L’Institut Henri Poincare 45 (2009), no. 3, 770–792. PDF
  26. (with Ross Pinsky) Ergodic behavior of diffusions with random jumps from the boundary. Stochastic Process. Appl. 119 (2009), no. 3, 864–881. PDF
  27. The Asymptotic Shift for the Principal Eigenvalue for Second Order Elliptic Operators on Bounded Domains under Various Boundary Conditions in the Presence of Small Obstacles.  Israel Journal of Mathematics 169 (2009), no. 2, 181–220. PDF
  28.  (with Ross Pinsky) Spectral analysis of a family of  second-order elliptic operators with nonlocal boundary condition indexed by a probability measure. Journal of Functional Analysis 251 (2007), no. 1, 122–140. PDF
  29. (with Ross Pinsky) Absolute continuity/singularity and relative entropy properties for probability measures induced by diffusions on infinite time intervals.  Stochastic Process. Appl. 115 (2005), no. 2, 179–206. PDF

17.5 (with Steven Miller) Appendix C (p. 158) to The Distribution of Gaps between Summands in Generalized Zeckendorf Decompositions (by Amanda Bower, Rachel Insoft, Shiyu Li, Steven J. Miller, Philip Tosteson), Journal of Combinatorial Theory, Series A Vol. 135 (2015), 130–160. PDF