Alan Hammond

Department of Statistics, University of Oxford
1 South Parks Road,
Oxford, U.K.


Research interests : probability theory, statistical mechanics, partial differential equations.

Publications :
- Critical exponents in percolation via lattice animals. ECP 10 (2005), 45-59.
- Fluctuation of planar Brownian loop capturing large area, with Yuval Peres. Trans. Amer. Math. Soc., to appear.
- The kinetic limit of a system of coagulating Brownian particles, with Fraydoun Rezakhanlou. Arch. Rational Mech. Anal. 185 (2007) 1 - 67.
- Kinetic limit for a system of coagulating planar Brownian particles, with Fraydoun Rezakhanlou. J. Stat. Phys. 124 (2006) 997-1040.
- Moment bounds for the Smoluchowski equation and their consequences, with Fraydoun Rezakhanlou. Comm. Math. Phys., to appear.
- Greedy lattice animals: geometry and criticality, Ann. Probab. 34 (2006), 2, 593-637.
- Coagulation, diffusion and the continuous Smoluchowski equation, with Mohammad Reza Yaghouti and Fraydoun Rezakhanlou. Stoc. Processes and their Applications, accepted.
- Monotone loop models and rational resonance, with Richard Kenyon. Probab. Theory and Related Fields, accepted.
- Biased random walks on Galton-Watson trees with leaves, with Gerard Ben Arous, Alexander Fribergh and Nina Gantert. Ann Probab, to appear.
- Power-law Polya's urn and fractional Brownian motion, with Scott Sheffield. Probab. Theory and Related Fields, accepted.
- Phase separation in random cluster models I: uniform upper bounds on local deviation. Comm. Math Phys., to appear.
- Phase separation in random cluster models II: the droplet at equilibrium, and local deviation lower bounds. Ann. Probab., to appear.
- Phase separation in random cluster models III: circuit regularity. J. Stat. Phys., to appear.
- Randomly biased walks on subcritical trees, with Gerard Ben Arous. CPAM, accepted.
- Stable limit laws for randomly biased walks on supercritical trees . Submitted.
- Phase transition for the speed of the biased random walk on the supercritical percolation cluster , With Alex Fribergh, submitted.
- Brownian Gibbs property for Airy line ensembles, With Ivan Corwin, submitted.
- Exit time tails from pairwise decorrelation in hidden Markov chains, with applications to dynamical percolation, With Elchanan Mossel and Gabor Pete.
- Infinite cycles in the random stirring model on trees.
- Sharp phase transition in the random stirring model on trees.

Teaching
Michaelmas 2009. - Applied probability.