Departments of Mathematics and Statistics, U.C. Berkeley



Alan Hammond

Associate Professor
Departments of Mathematics and Statistics
University of California at Berkeley

791 Evans Hall
Berkeley, CA
94720-3840 USA


Email: :

Photo


Leave to remain?

Vladimir: Well? Shall we go?
Estragon: Yes, let's go.

They do not move.

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., 67 , no. 2, 173--245, (2014)
    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., 195 , 441--508, (2014)
    21. Sharp phase transition in the random stirring model on trees.
      Probab. Theory and Related Fields, 161 , no. 3-4, 429--448, (2015)
    22. Local time on the exceptional set of dynamical percolation, and the Incipient Infinite Cluster.
      With Gabor Pete and Oded Schramm.
      Ann. Probab., 43 , no. 6, 2949--3005, (2015)
    23. On the probability that self-avoiding walk ends at a given point.
      With Hugo Duminil-Copin, Alexander Glazman and Ioan Manolescu.
      Ann. Probab., 44 , no. 2, 955--983, (2016)
    24. KPZ Line Ensemble.
      With Ivan Corwin.
      Probab. Theory and Related Fields, 166 , no. 1-2, 67--185, (2016)
    25. An upper bound on the number of self-avoiding polygons via joining .
      Ann. Probab., to appear.

    Preprints