Research

My research is in probability theory. My primary interests are Gibbs measures, MCMC and combinatorial statistics. A major focus of my work has been on understanding the mixing times of Markov chains, particularly the Glauber dynamics on trees and random graphs and how it relates to phases transition of the Gibbs measue. I am also intereted in the reconstruction problem on trees for a number of Gibbs distributions.

[12]Cutoﬀ phenomena for random walks on random regular graphs 2008 (with E. Lubetzky) Preprint

[11]Reconstruction of symmetric Potts Models 2008 Preprint

[10]Mixing time of exponential random graphs (with G. Bresler and S. Bhamidi) Proceedings of IEEE Symposium on Foundations of Computer Science 2008, p 803-812 Preprint

[9]Exact conditions for no ruin for the generalised Ornstein-Uhlenbeck process 2008 (with D. Bankovsky) To appear Stochastic Processes and Applications Preprint

[8]Reconstruction of Random Colourings 2008 To appear Communications of Mathematical Physics Preprint

[7]Reconstruction of Markov Random Fields from Samples: Some Easy Observations and Algorithms 2008 (with G. Bresler and E. Mossel) Proceedings of RANDOM 2008 Preprint

[6]Gibbs Rapidly Samples Colorings of G(n,d/n) 2008 (with E. Mossel) To appear Probability Theory and Related Fields Preprint

[5]Rapid Mixing of Gibbs Sampling on Graphs that are Sparse on Average (with E. Mossel) Procedings of ACM-SIAM Symposium on Discrete Algorithms 2008, p238-247. To appear in Random Structures and Algorithms. PDF Preprint

[4]Uniqueness Thresholds on Trees and Graphs (To appear in the Annals of Applied Probability) Preprint

[3]A Cautionary Note on Modeling with Fractional Levy Flights (with C.C. Heyde), Physica A, 387, (2008) 5024-5032 Link

[2]Non-Standard Limit Theorem for Infinite Variance Functionals. (with C.C. Heyde), Annals of Probability, 36, (2008) 796-805. Link

[1]Integrated Fractional White Noise, Journal of Applied Probability, 44, (2007), 393-408. Link

Allan Sly

Allan Sly

Research