Publications

Preprints

1. Quasi-stationary behavior of the stochastic FKPP equation on the circle. With Oliver Tough. Under review.

2. Intertwining the Busemann process of the directed polymer model. With E. Bates and T. Seppäläinen. Under review.

3. A new path method for exponential ergodicity of Markov processes on Z^d, with applications to  stochastic reaction networks. With D. Anderson, D. Cappelletti and J. Kim. Under review.

4. Correlation of coalescence times in a diploid Wright-Fisher model with recombination and selfing. With D. Kogan, D. Diamantidis and J. Wakeley. Under review.

5. Sensitivity of Tropical Cyclone Rapid Intensification Onset to the Vortex Structure and the Large-scale Environment. With Chanh Kieu, Peter Finocchio, Yi Jin, James D. Doyle, Xander Lowry. Submitted.

Publications

6. Latent mutations in the ancestries of alleles under selection. With J. Wakeley. Theoretical population biology, Vol 158, 2024.

7. Bursts of coalescence within population pedigrees whenever big families occur. With D. Diamantidis, M. Birkner and J. Wakeley. Genetics, 2024. (Featured article in the May 2024 issue).

8. Recurrent mutation in the ancestry of a rare variant. With J. Wakeley*, E. Koch and S. Sunyaev. Genetics. Vol 224 (3), 2023  (*Joint first author).

9. Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles. With Q. Liang, Y. J. Yang, W.-C. Lo. PLOS Computational Biology, 19(10), 2023.

10. Constrained Langevin approximation for the  Togashi-Kaneko model of autocatalytic reactions. With Y. J. Yang and C. Yuan. Mathematical Biosciences and Engineering (special issue in stochastic methods for biological systems). Vol20 (3), 2023. 

11. Three-dimensional shear driven turbulence with Levy noise at the boundary. With A. Pakzad, K. Tawri and R.Temam. Probability, Uncertainty and Quantitative Risk. Vol 8 (1). 2023.

12. An impossibility result for phylogeny reconstruction from k-mer counts. With B. Legried and S. Roch. Annals of Applied Probability. 32(6), 2022.

13. On the Existence of low-dimensional chaos of the tropical cyclone intensity in an idealized axisymmetric simulation. With C. Kieu and W. Cai. Journal of the Atmospheric Sciences. 2022.

14. Sensitivity of Tropical Cyclone Intensity Variability to Different Stochastic Parameterization Methods. With C. Kieu and M. Patra. Frontiers in Earth Science. 2022.

15. Stochastic PDEs on graphs as scaling limits of discrete interacting systems. Bernoulli. 27(3), 2021.

16. Wave propagation for reaction-diffusion equations on infinite trees. With Wenqing Hu and Grigory Terlov. Communications in Mathematical Physics. 384, 2021.

17. Three-dimensional shear driven turbulence with noise at the boundary. With Mike Jolly and Ali Pakzad. Nonlinearlity. Vol 34 (7), 2021.

18. Hitting time of rapid intensification onset in hurricane-like vortices. With C. Kieu, D. Sakellariou and M. Patra. Physics of Fluids, 33(9) 2021. 

19. Modeling atmospheric data and identifying dynamics large temporal data-driven modeling of air pollutants. With J. Rubio-Herrero and C. O. Marrero. Journal of Cleaner Production, 2021.

20. Modelling the impact of travel restrictions on COVID-19 cases in Hong Kong in early 2020. With Pak Leung Ho, et al. BMC Public Health. 2021.

21. Joint distribution of Busemann functions in the exactly solvable corner growth model. With Timo Seppäläinen. Probability and Mathematical Physics. Vol 1(1), 55-100, 2020.

22. Impossibility of consistent distance estimation from sequence lengths under the TKF91 model. With Brandon Legried and Sebastien Roch. Bulletin of Mathematical Biology. Vol 82 (9), 2020.

23. Statistically consistent and computationally efficient inference of ancestral DNA sequences in the TKF91 model under dense taxon sampling. With Sebastien Roch. Bulletin of Mathematical Biology. Vol 82 (2), 2020.

24. Stochastic Variability of Tropical Cyclone Intensity at the Maximum Potential Intensity Equilibrium. With Phuong Nguyen and Chanh Kieu. Journal of the Atmospheric Sciences. 77 (9), 3105-3118, 2020.

25. Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees. With Sebastien Roch. Electronic Journal of Probability, Vol. 23 (47), 1-24, 2018.

26. Stochasticity, selection, and the evolution of cooperation in a two-level Moran model of the Snowdrift Game. With Brian McLoone, Adam Pham, Smead Rory and Laurence Loewe. Complexity. Vol. 2018.

27. Systems of interacting diffusions with partial annihilations through membranes. With Z.-Q. Chen. Annals of Probability. Vol.45, 100-146, 2017.

28. Hydrodynamic limits and propagation of chaos for interacting random walks in domains.  With Z.-Q. Chen. Annals of Applied Probability. Vol 27 (3 ) 1299-1371, 2017.

29. Ellipsoidal Brownian self-driven particles in a magnetic field. With On Shun Pak and Mario Sandoval. Physical Review E, 95 (3), 032605, 2017.

30. Uniform in time interacting particle approximations for nonlinear equations of Keller-Segel type.  With Amarjit Budhiraja. Electronic Journal of Probability, Vol. 22 (8), 1-37, 2017.

31. Genealogies in expanding populations. With Rick Durrett. Annals of Applied Probability. Vol. 26 (6), 3456-3490, 2016.

32. Discrete approximations to local times for reflected diffusions. Electron. Commun. Probab. Vol. 21 (16), 2016.

33. Large deviations for Brownian particle systems with killing. With Amarjit Budhiraja and Ruoyu Wu. Journal of Theoretical Probability. 1-40, 2016.

34. Fluctuation limits for systems of interacting diffusions with partial annihilations through membranes. With Z.-Q. Chen. Journal of Statistical Physics. 164, 890-936, 2016.

35. Mucins and associated glycan signatures in colon adenomacarcinoma sequence: prospective pathological implications for early diagnosis of colon cancer.  With Shiv Ram Krishn, et al. Cancer Letters, 374 (2), 304-314, 2016.

36. Functional central limit theorem for Brownian particle systems in domains with boundary condition. With Z.-Q. Chen. Journal of Functional Analysis. Vol 269 (12), 3765-3811, 2015.

37. Scaling limits of interacting diffusions in domains. With Z.-Q. Chen. Front. Math. China, 9 (4): 717–736, 2014.

Books

38. Pui Ching invitational mathematics competition: questions and answers. With Kin Hang Chan and Ka Ho Law. Pui Ching Education Centre, 2008.

Unpublished manuscripts 

1. Interacting particle systems with partial annihilation through membranes. PhD thesis 2014.

2. Wulff flow and Steiner polynomials for ovaloids. Master thesis 2005.

3. Correlation function methods for a system of annihilating Brownian particles. Expository note.

Slides and Posters

1. Indiana Research Experience for Undergraduate (REU) Keynote Lecture 2023 

2. Wave propagation for reaction-diffusion equations on random trees.

3. Identification and estimation for Markov processes on phylogenetic trees.

4. Stochastic spatial models for complex systems.

5. Stochastic spatial model for virus co-infection and defective interfering particles.