Research

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Publications and Preprints

My recent focus is on quasistationary distributions.

  • Most recent (but not always up to date) preprints are available on my ArXiv page.
  • "*" represents an undergraduate collaborator.
    1. I.B. and Ningwei Jiang. Representation and Characterization of Quasistationary Distributions for Markov Chains. Submitted. arxiv:2402.11154
    2. I.B. and Rinaldo Schinazi. Can a single migrant per generation rescue a dying population? To appear in Advances in Applied Mathematics. arxiv:2304.06478
    3. I.B, Clayton Allard*, Shrikant Chand*, Van Hovenga*, Edith Lee*, Julia Shapiro*. Quasistationary Distribution for the Invasion Model on a Complete Bipartite Graph. Journal of Stochastic Analysis: Vol. 5: No. 1, Article 2. arxiv:2204.10287
    4. I.B. and Rinaldo Scinazi. Self-similarity in an exchangeable site-dynamics model. Journal of Statistical Physics volume 188, Article number: 17 (2022).  arxiv:2101.00705
    5. I.B. and  Mason DiCicco*. Greedy Coupling of 3-State Markov Chains, submitted
    6. I.B. and  SangJoon Lee. Quasi-Limiting Behavior of Drifted Brownian Motion. ALEA, Lat. Am. J. Probab. Math. Stat. 19, 813–838 (2022). arxiv:2001.04523
    7. I.B, Hugo Panzo, Philip Speegle* and Oliver Vandenberg*. Quasistationary Distributions for the Voter Model on Complete Bipartite Graphs. ALEA, Lat. Am. J. Probab. Math. Stat. 18 (2021), 421–437. arxiv:2004.1018
    8. I.B, Jonah Green*, Taylor Meredith*, Hugo Panzo and Xioran Tan*. Finite-Memory Elephant Random Walk and the Central Limit Theorem for Additive Functionals. Braz. J. Probab. Stat. 35(2) (2021),242–262
    9. I.B.,  Carter Bedsole* and Grace O’Neil*. Power-Law Tails in a Fitness-Driven Model for Biological Evolution. Submitted.  arxiv:2001.00960
    10. I.B and  Behrang Forghani. On Transformations of Markov Chains and Poisson Boundary. Trans. Amer. Math. Soc.373 (2020), 2207–2227.  arxiv:1909.11217
    11. I.B.,  Alexander Roitershtein and Rinaldo Schinazi.  A Random Walk with Catastrophes, Elec. J. of Probability 24 (2019), no. 28, 1–21. arxiv:1709:04780
    12. I.B. and  Roger Silva. On a Local Version of the Bak-Sneppen Model,  Journal of Statistical Physics, Vol. 173 (2) (2018), 362–380. arxiv:1609.04420
    13. I.B and  Hugo Panzo. On the Subcritical Phase for a Homopolymer Model. Communications on Stochastic Analysis, Vol. 11 (2017), No. 4, 425–456 arxiv:1803.09335
    14. I.B and  Rinaldo Schinazi. A Stochastic Model for the Evolution of a Quasispecies , Journal of Statistical Physics, 162(2), 415–425
    15. I.B and Steven J. Miller. A Probabilistic Approach to Generalized Zeckendorf Decompositions . SIAM J. Discrete Math, Vol. 30 (2016), No. 2, 1302–1332. arxiv:1405.2379
    16. I.B. and Steven J. Miller. p. 158 in 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
    17. I.B.,  Hugo Panzo, and Elizabeth Tripp*. Efficient Coupling for Random Walk with Redistribution.  arxiv:1410.8234
    18. I.B. On Independence and Determination of Probability Measures,  Journal of Theoretical Probability Vol. 28(3), 968–975
    19. I.B. Coupling for Drifted Brownian Motion on an Interval with Redistribution from the Boundary,  Electronic Communications in Probability Vol. 19 (2014), no. 16, 1–11
    20. I.B., Diana Hay and Alexander Roitershtein. On Wallis-type products and Polya’s urn schemes,  American Mathematical Monthly Vol. 121, No. 5, 422–432
    21. I.B and Keith Conrad.  Maclaurin’s Inequality and a Generalized Bernoulli Inequality ,   Mathematics Magazine Vol. 87, No. 1, 14–24
    22. I.B. An Empirical Process Interpretation of a Model of Species Survival, Stochastic Process.  Appl. 123 (2013), 475–489
    23. I.B. Principal Eigenvalue for Brownian Motion on a Bounded Interval with Degenerate Instantaneous Jumps,  Electronic Journal of Probability, Vol. 17 (2012), no. 87, 1–13
    24. I.B. and Michael Neumann. Probabilistic Approach to Perron Root, the Group Inverse, and Applications ,  Linear and Multilinear Algebra, Vol. 60 (2012), no. 1,  39–63
    25. I.B.,  Michael Neumann and Olga Pryporova. Inequalities for Functions of Transition Matrices,  Linear Algebra and its Applications, Vol. 436 (2012), no. 2, 335–348
    26. I.B., Anastasios Matzavinos and Alexander Roitershtein. On a species survival model , Electronic Communications in Probability, Vol. 16 (2011) paper 22, 226–233
    27. I.B., 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
    28. I.B.,  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
    29. I.B. Large Deviations For Partition Functions of Directed Polymers in an IID Field. Annales de L’Institut Henri Poincare 45 (2009), no. 3, 770–792
    30. I.B. and Ross Pinsky. Ergodic behavior of diffusions with random jumps from the boundary. Stochastic Process. Appl. 119 (2009), no. 3, 864–881
    31. I.B. 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
    32. I.B. and 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

Presentations and Posters

Introductory talks