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Gaussian free fields for mathematicians

Dec 4, 2003
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Abstract: (submitter)
The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are appropriately scaled), the GFF is the limit of many incrementally varying random functions on d-dimensional grids. We present an overview of the GFF and some of the properties that are useful in light of recent connections between the GFF and the Schramm-Loewner evolution.
  • [Ada75]
    Sobolev spaces
    • Robert A. Adams
  • [BDG01]
    Erwin Bolthausen, Jean-Dominique Deuschel, and Giambattista Giacomin. Entropic repulsion and the maximum of the twodimensional harmonic crystal
      • Annals Probab. 29 (2001) 1670-1692
  • [BDZ00]
    Erwin Bolthausen, Jean Dominique Deuschel, and Ofer Zeitouni. Absence of a wetting transition for a pinned harmonic crystal in dimensions three and larger
      • J.Math.Phys. 41 (2000) 1211-1223
  • [BI97]
    Erwin Bolthausen and Dmitry Ioffe. Harmonic crystal on the wall: a microscopic approach
      • Commun.Math.Phys. 187 (1997) 523-566
  • [Car90]
    Conformal invariance and statistical mechanics. In Champs, cordes et phénomènes critiques (Les Houches, 1988), pages 169-245
    • John L. Cardy
  • [DFMS97]
    Philippe Di Francesco, Pierre Mathieu, and David Sénéchal. Conformal field theory. Graduate Texts in Contemporary Physics
  • [Dur96]
    Richard Durrett. Probability: theory and examples. Duxbury Press, Belmont, CA, second edition
  • [Dyn83]
    Markov processes as a tool in field theory
    • E.B. Dynkin
      • J.Funct.Anal. 50 (1983) 167-187
  • [Dyn84a]
    Gaussian and non-Gaussian random fields associated with Markov processes
    • E.B. Dynkin
      • J.Funct.Anal. 55 (1984) 344-376
  • [Dyn84b]
    Polynomials of the occupation field and related random fields
    • E.B. Dynkin
      • J.Funct.Anal. 58 (1984) 20-52
  • [FFS92]

    Random walks, critical phenomena, and triviality in quantum field theory

  • [Gia00]
    Giambattista Giacomin. Anharmonic lattices, random walks and random interfaces. Recent research developments in statistical physics, Transworld
      • Research I 97 (2000) 118
  • [GJ87]
    James Glimm and Arthur Jaffe. Quantum physics. SpringerVerlag, New York, second edition,. A functional integral point of view
  • [GOS01]
    Giambattista Giacomin, Stefano Olla, and Herbert Spohn. Equilibrium fluctuations for ∇φ interface model
      • Annals Probab. 29 (2001) 1138-1172
  • [Gro67]
    Leonard Gross. Abstract Wiener spaces. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif.,/66), Vol. II: Contributions to Probability Theory, Part 1, pages 31-42. Univ. California Press, Berkeley, Calif., 1967
  • [Hen99]

    Conformal invariance and critical phenomena

  • [HP]
    Xiaoyu Hu and Yuval Peres. Thick points of the gaussian free field. [in preparation]
    • [Jan97]
      Svante Janson. Gaussian Hilbert spaces, volume 129 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge
    • [Ken01]
      Richard Kenyon. Dominos and the Gaussian free field
        • Annals Probab. 29 (2001) 1128-1137
    • [NS05]
      Yu. Netrusov and Yu. Safarov. Weyl asymptotic formula for the Laplacian on domains with rough boundaries
        • Commun.Math.Phys. 253 (2005) 481-509
    • [She05]
      Scott Sheffield. Random surfaces. Astérisque, 304