MAILING ADDRESS:  Department of Mathematics KAP 108, USC, 

Los Angeles, California 90089-2532

PHONE: (213) 740-3797

FAX: (213) 740-2424

OFFICE: KAP 424E

EMAIL: alexandr (at) usc (dot) edu

Areas of interest:

• Probability models from physics (statistical mechanics)--percolation, Ising model, Potts model, first passage percolation, and other models on a lattice.  Polymers, Gibbs distributions, interfaces.
  
• Subadditive Euclidean functionals on random point sets--minimal spanning trees, traveling salesman problem.
• empirical processses and probability in Banach spaces.

Biographical

BS, University of Washington, 1979

Ph.D., MIT, 1982

Member, Mathematical Sciences Research Institute, Berkeley, 1982-1983

NSF Postdoctoral Fellow and Acting Assistant Professor, Department of Mathematics and Department of Statistics, University of Washington, 1983-1986

Assistant Professor of Mathematics, USC, 1986-1990

Associate Professor of Mathematics, USC, 1990-1996

Professor of Mathematics, USC, 1996-present

• Layering in the Ising model.  With F. Dunlop and S. Miracle-Sole.  Available at http://arxiv.org/abs/0911.2105 .  27 pages.  (2009)
  
• Layering and wetting transitions for an SOS interface.  With F. Dunlop and S. Miracle-Sole.  Available at http://arxiv.org/abs/0908.0321 .  54 pages.  (2009)
  
• Equality of critical points for polymer depinning transitions with loop exponent one.  With N. Zygouras.  To appear in Annals of Applied Probability.  Available at http://arxiv.org/abs/0811.1902 . 10 pages.  (2008)
  
• Quenched and annealed critical points in polymer pinning models.  With N. Zygouras.  Communications in Mathematics Physics 291, 659 - 689.  Available at http://arxiv.org/abs/0805.1708 .  33 pages.  (2008)
  
• Ivy on the ceiling:  first-order polymer depinning transitions with quenched disorder.  Markov Processes and Related Fields 13, 663 - 680.  Available at http://arxiv.org/abs/math.PR/0612625.  15 pages.  (2007)
  
• The effect of disorder on polymer depinning transitions.  Communications in Mathematical Physics 279, 117 - 146.  Available at http://arxiv.org/abs/math.PR/0610008.  31 pages.  (2008)
  
• Pinning of polymers and interfaces by random potentials.  With V. Sidoravicius.  Annals of Applied Probability 16, 636 - 669.  Available at http://arxiv.org/abs/math.PR/0501028 . 33 pages.  (2006)
  
• Colligative properties of solutions: I. Fixed concentrations. With M. Biskup and L. Chayes.  Journal of Statistical Physics 119, 479 - 507.  Available at http://arxiv.org/abs/math-ph/0407034.  (2005)
• Colligative properties of solutions:  II. Vanishing concentrations.  With M. Biskup and L. Chayes.  Journal of Statistical Physics 119, 509 - 537.  Available at http://arxiv.org/abs/math-ph/0407035.  (2005)
  
• Separated-occurrence inequalities for dependent percolation and Ising models.  Available at  http://arxiv.org/abs/math.PR/0210015  .  38 pages. (2002)
• Mixing properties and exponential decay for lattice systems in finite volumes.  Annals of Probability 32, 441 - 487.  Available at  http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=01-309  .  (2004)
• Lower bounds for boundary roughness for droplets in Bernoulli percolation.  With H. Uzun.  Probability Theory and Related Fields 127, 62 - 88.  Available at  http://arxiv.org/abs/math.PR/0210016  .  (2003)
• The spectral gap of the 2-D stochastic Ising model with mixed boundary conditions.  With N. Yoshida.  Journal of Statistical Physics 104, 89 - 109.  Available at  http://front.math.ucdavis.edu/math.PR/0008201 .  (2001)
• The spectral gap of the 2-D stochastic Ising model with nearly single-spin boundary conditions.   Journal of Statistical Physics 104, 59 - 87.  Available from  http://www.ma.utexas.edu/mp_arc/  as preprint #00-230.  (2001)
• Cube-root boundary fluctuations for droplets in random cluster models. Communications in Mathematical Physics 224, 733 - 781.  Available from  http://www.ma.utexas.edu/mp_arc/  as preprint #00-19.  72 pages.  (2001)
• Power-law corrections to exponential decay of connectivities and correlations in lattice models. Annals of Probability 29, 92 - 122.  Available from  http://www.ma.utexas.edu/mp_arc/  as preprint #00-245.  (2001)
• The asymmetric random cluster model and comparison of Ising and Potts models. Probability Theory and Related Fields  120, 395-444.  Available from  http://www.ma.utexas.edu/mp_arc/  as preprint #00-81.  (2001).
• On weak mixing in lattice models. Probability Theory and Related Fields 110, 441-471 (1998).
• Non-perturbative criteria for Gibbsian uniqueness. With L. Chayes. Communications in Mathematical Physics 198, 447-464 (1997).
• Approximation of subadditive functions and convergence rates in limiting-shape results. Special Invited Paper. Annals of Probability 25, 30-55 (1997).
• Boundedness of level lines for two-dimensional random fields. Annals of Probability  24, 1653-1674 (1996).
• Percolation and minimal spanning forests in infinite graphs. Annals of Probability 23, 87-104 (1995).
• Rates of convergence of means for distance-minimizing subadditive Euclidean functionals. Annals of Applied Probability 4, 902-922 (1994).
• The rate of convergence of the mean length of the longest common subsequence, Annals of Applied Probability 4, 1074-1082 (1994).
• Percolation of level sets for two-dimentional random fields with lattice symmetry. With S.A. Molchanov. Journal of Statistical Physics 77, 627-634 (1994).

Courses--Fall 2009

MATH 605 Topics in Probability

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