Path Coupling and Aggregate Path Coupling (with Y. Kovchegov) SpringerBriefs in Probability and Mathematical Statistics. ISBN 978-3-319-77018-5 (2018) 

Journal Publications

• Gelation in Vector Multiplicative Coalescence and Extinction in Multi-Type Poisson Branching Processes (with H. Aravinda, Y. Kovchegov, and A. Sarkar) Under review.

• Extension to the Beraha-Kahane-Weiss Theorem with Applications (with J. Brown), Contributions to Discrete Mathematics, To appear.
  
  

• Multidimensional Lambert-Euler Inversion and Vector-Multiplicative Coalescent Processes (with Y. Kovchegov), Journal of Statistical Physics, Volume 190, Number 188 (2023).
  
  

• Cross-Multiplicative Coalescent Processes and Applications (with Y. Kovchegov and A. Yambartsev), ALEA, Latin American Journal of Probability and Mathematical Statistics, Volume 18, pages 81-106 (2021).
  
  

• Justice as Fair Division (with I. Bartrum and K. Nyman), Pepperdine Law Review, Volume 45: 531 (2018).
  
  

• The Aggregate Path Coupling Method for the Potts Model on Bipartite Graph (with J. Hernandez and Y. Kovchegov), Journal of Mathematical Physics, Volume 58, Number 2, 023303 (2017).
  
  

• Mixing Times for the Rook's Walk via Path Coupling (with C. McLeman, J. Rahmani*, and M. Sutter*), Involve , Volume 10, Number 1, pages 51-64 (2017).
  
  

• Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods (with Y. Kovchegov), Journal of Statistical Physics, Volume 161, Number 3, pages 553-576 (2015).
  
  

• Polynomial Representation for the Expected Length of Minimal Spanning Trees (with J. Nishikawa* WU '10 and C. Starr), Pi Mu Epsilon Journal, Volume 13, Number 6, pages 357–365 (2012).
  
  

• Mixing Times for the Mean-Field Blume-Capel Model via Aggregate Path Coupling (with Y. Kovchegov and M. Titus), Journal of Statistical Physics, Volume 144, Number 5, pages 1009-1027 (2011).
  
  

• Asymptotic Behavior of the Finite-Size Magnetization as a Function of the Speed of Approach to Criticality (with R. S. Ellis and J. Machta), Annals of Applied Probability, Volume 20, Number 6, pages 2118–2161 (2010).
  
  

• Asymptotic Behavior of the Magnetization near Critical and Tricritical Points via Ginzburg-Landau Polynomials (with R. S. Ellis and J. Machta), Journal of Statistical Physics, Volume 133, Number 1, pages 101-129 (2008).
  
  

• Ginzburg-Landau Polynomials and the Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points (with R. S. Ellis and J. Machta) 75-page Latex manuscript. This unpublished paper contains details of proofs and calculations omitted from the paper listed in the preceding bullet. It is posted at http://arxiv.org/abs/0803.0178.
  
  

• Multiple Critical Behavior of Probabilistic Limit Theorems in the Neighborhood of a Tricritical Point (with M. Costeniuc and R. S. Ellis), Journal of Statistical Physics, Volume 127, Number 3, 495–552 (2007).
  
  

• Analysis of Phase Transitions in the Mean-Field Blume-Emery-Griffiths Model (with R. S. Ellis and H. Touchette), Annals of Applied Probability, Volume 15, Number 3, pages 2203–2254 (2005).
  
  

• A Statistical Approach to the Asymptotic Behavior of a Class of Generalized Nonlinear Schrödinger Equations (with R. S. Ellis, R. Jordan, and B. Turkington), Communications in Mathematical Physics, Volume 244, Number 1, pages 187–208 (2004).

* indicates student co-author