Gaussian free fields for mathematicians

Probability Theory and Related Fields

Volumn 139, Issue 3-4, 2007, Pages 521-541

  Sheffield, Scott ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547233310     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-006-0050-1     Document Type: Article

References (24)

1. Adams, R.A.: Sobolev Spaces. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, (1975) Pure and Applied Mathematics, vol. 65
2. Bolthausen E., Ioffe D. (1997). Harmonic crystal on the wall: a microscopic approach. Comm. Math. Phys. 187(3): 523-566
3. Bolthausen E., Deuschel J.-D., Giacomin G. (2001). Entropic repulsion and the maximum of the two-dimensional harmonic crystal. Ann. Probab. 29(4): 1670-1692
4. Bolthausen, E., Deuschel, J-D., Zeitouni, O.: Absence of a wetting transition for a pinned harmonic crystal in dimensions three and larger. J. Math. Phys., 41(3), 1211-1223, (2000). Probabilistic techniques in equilibrium and nonequilibrium statistical physics
5. Cardy, J.L.: Conformal invariance and statistical mechanics. In: Champs, cordes et phénomènes critiques (Les Houches, 1988), pp. 169-245. North-Holland, Amsterdam (1990)
6. Di Francesco P., Mathieu P., Sénéchal D. (1997). Conformal Field Theory. Graduate Texts in Contemporary Physics., Springer Berlin Heidelberg New York
7. Durrett R. (1996). Probability: Theory and Examples, 2nd edn. Duxbury Press, Belmont, CA
8. Dynkin E.B. (1983). Markov processes as a tool in field theory. J. Funct. Anal. 50(2): 167-187
9. Dynkin E.B. (1984). Gaussian and non-Gaussian random fields associated with Markov processes. J. Funct. Anal. 55(3): 344-376
10. Dynkin E.B. (1984). Polynomials of the occupation field and related random fields. J. Funct. Anal. 58(1): 20-52
11. Fernández, R., Fröhlich, J., Sokal, A.D.: Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory. Texts and Monographs in Physics. Springer, Berlin Heidelberg Newyork (1992).
12. 4. Ann. Phys. 147(1): 198-243
13. Giacomin G. (2000). Anharmonic lattices, random walks and random interfaces. Recent Research Developments in Statistical Physics, Transworld Research I: 97-118
14. Giacomin G., Olla S., Spohn H. (2001). Equilibrium fluctuations for ∇φ interface model. Ann. Probab. 29(3): 1138-1172
15. Glimm J., Jaffe A. (1987). Quantum Physics, 2nd edn. Springer Berlin Heidelberg, New York A functional integral point of view
16. Gross, L.: Abstract Wiener spaces. In: Proc. Fifth Berkeley Sympos. Math. Statist., Probability (Berkeley, Calif., 1965/66), vol. II: Contributions to Probability Theory, Part 1, pp. 31-42. University of California Press, Berkeley (1967)
17. Henkel M. (1999). Conformal Invariance and Critical Phenomena. Texts and Monographs in Physics, Springer Berlin Heidelberg Newyork
18. Hu, X., Peres, Y.: Thick points of the gaussian free field (in preparation)
19. Janson S. (2001). Dominos and the Gaussian free field. Ann. Probab. 29(3): 1128-1137
20. Kenyon R. (2001). Dominos and the Gaussian free field. Ann. Probab. 29(3): 1128-1137
21. Naddaf A., Spencer T. (1997). On homogenization and scaling limit of some gradient perturbations of a massless free field. Comm. Math. Phys. 183(1): 55-84
22. Netrusov Yu., Safarov Yu. (2005). Weyl asymptotic formula for the Laplacian on domains with rough boundaries. Comm. Math. Phys. 253(2): 481-509
23. Schramm, O., Sheffield, S.: Contour lines of the two-dimensional discrete Gaussian free field, arXiv:math.PR/0605337
24. Sheffield, S.: Random surfaces. Astéisque, 304 (2005)