Department of Statistics, Oxford University


Alan Hammond

Department of Statistics
1 South Parks Road
OX2 3TG
Oxford United Kingdom

My new home page is math.berkeley.edu/~alanmh Email: :
Office : 308
Telephone : (+44) 1865 272 599
Photo

Research

My research concerns probability theory, statistical mechanics and partial differential equations: a research overview.

    Notes from a graduate course

    During the autumn of 2012, I gave a graduate couse at the University of Geneva concerning the kinetic limit derivation of Smoluchowski's coagulation-diffusion PDE,
    which forms the basis of this survey:
  1. Coagulation and diffusion: a probabilistic perspective on the Smoluchowski PDE.


    Publications

    1. Critical exponents in percolation via lattice animals.
      Electron. Comm. Probab., 10, no.4, 45--59 (2005).
    2. Fluctuation of planar Brownian loop capturing large area.
      With Yuval Peres.
      Trans. Amer. Math. Soc., 360, no. 12, 6197--6230 (2008).
    3. The kinetic limit of a system of coagulating Brownian particles.
      With Fraydoun Rezakhanlou.
      Arch. Rational Mech. Anal., 185, 1--67 (2007).
    4. Kinetic limit for a system of coagulating planar Brownian particles.
      With Fraydoun Rezakhanlou.
      J. Stat. Phys., 124, 997--1040 (2006).
    5. Moment bounds for the Smoluchowski equation and their consequences.
      With Fraydoun Rezakhanlou.
      Comm. Math. Phys., 276, no. 3, 645--670 (2007).
    6. Greedy lattice animals: geometry and criticality.
      Ann. Probab., 34, no.2, 593--637, (2006).
    7. Coagulation, diffusion and the continuous Smoluchowski equation.
      With Mohammad Reza Yaghouti and Fraydoun Rezakhanlou.
      Stochastic Process. Appl., 119 , no. 9, 3042--3080, (2009).
    8. Monotone loop models and rational resonance.
      With Richard Kenyon.
      Probab. Theory and Related Fields, 150, no. 3-4 ,613--633, (2011)
    9. Biased random walks on Galton-Watson trees with leaves.
      With Gerard Ben Arous, Alexander Fribergh and Nina Gantert.
      Ann. Probab., 40, no. 1, 280--338, (2012).
    10. Power-law Polya's urn and fractional Brownian motion.
      With Scott Sheffield.
      Probab. Theory and Related Fields, 157, no. 3, 691--719, (2013).
    11. Phase separation in random cluster models I: uniform upper bounds on local deviation.
      Comm. Math Phys., 310 , no. 2, 455--509, (2012)
    12. Phase separation in random cluster models II: the droplet at equilibrium, and local deviation lower bounds.
      Ann. Probab., 40 , no. 3, 921--978, (2012)
    13. Phase separation in random cluster models III: circuit regularity.
      J. Stat. Phys., 142, no. 2, 229--276, (2011)
    14. Randomly biased walks on subcritical trees.
      With Gerard Ben Arous.
      Comm. Pure Appl. Math., 65 , no. 11, 1481--1527, (2012)
    15. Stable limit laws for randomly biased walks on supercritical trees.
      Ann. Probab., 41 , no. 3A, 1694--1766, (2013)
    16. Exit time tails from pairwise decorrelation in hidden Markov chains, with applications to dynamical percolation.
      With Elchanan Mossel and Gabor Pete.
      Electron. J. Probab., 17 , article 68, 1--16, (2012)
    17. Phase transition for the speed of the biased random walk on the supercritical percolation cluster.
      With Alex Fribergh.
      Comm. Pure Appl. Math., to appear.
    18. Infinite cycles in the random stirring model on trees.
      Bulletin of the Institute of Mathematics, Academia Sinica, Special Issue in honour of S.R.S. Varadhan's 70th birthday, 8, no. 1, 85--104, (2013)
    19. Self-avoiding walk is sub-ballistic.
      With Hugo Duminil-Copin.
      Comm. Math. Phys., 324 , no. 2, 401--423, (2013)
    20. Brownian Gibbs property for Airy line ensembles.
      With Ivan Corwin.
      Invent. Math., to appear.
    21. Sharp phase transition in the random stirring model on trees.
      Probab. Theory and Related Fields, to appear.

    Preprints

    1. Local time on the exceptional set of dynamical percolation, and the Incipent Infinite Cluster.
      With Gabor Pete and Oded Schramm.
      Submitted.
    2. On the probability that self-avoiding walk ends at a given point.
      With Hugo Duminil-Copin, Alexander Glazman and Ioan Manolescu.
      Submitted.
    3. KPZ Line Ensemble.
      With Ivan Corwin.
      Submitted.