Publications and Preprints:
Rigorous Bounds on the Emptiness Formation Probability in Quantum XXZ Models, w/ S. Ng, and S. Starr, In Preparation.
Localization in Linearly Reinforced Random Walks (and Vertex Reinforced Jump Processes),w/ O. Angel and G. Kozma.
Random Field Induced Order in Low Dimension, Announcement; summarizes two previous entries. To appear in Europhysics Letters.
Random Field Induced Order in Low Dimension II, In Preparation; The interesting case: Dimension 2 with any constant boundary condition.
Random Field Induced Order in Low Dimension I, Demonstrates the basic method in the simplest case: Dimension 3 with optimal boundary condition.
Absence of Ferromagnetism in Continuous-Spin Systems with Long-Range Antialigning Forces, w/ M. Biskup, J. Stat. Phys. (2011), Volume 144, No. 4, Pages 731-748.
On Random Field Induced Ordering in the Classical XY Model, J. Stat. Phys. (2011), Volume 142, No. 1, Pages 11-42.
Simple Random Walks on Long Range Percolation Clusters II: Scaling Limits, w/ A. Sly; Accepted for Publication, Annals of Probability.
Simple Random Walks on Long Range Percolation Clusters I: Heat Kernel Bounds, w/ A. Sly; Probability Theory and Related Fields (4 August 2011), pp. 1-34
Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window, w/ N. Bhatnagar, A. Sen, E. Mossel; Order 5 January 2012
The Phase Diagram of the Mean Field Transverse Ising Model,w/ L. Chayes, D.Ioffe, A. Levit; J. Stat. Phys. 133, 1, Oct. 2008.
Thermodynamics and Universality for Mean Field Quantum Spin Glasses, Comm. Math. Phys. 274, 3, September 2007.
Mean-field driven first-order phase transitions in systems with long-range interactions, w/ M. Biskup, L. Chayes; J. Statist. Phys. 122, no. 6, 1139-1193 2006.