Phase transition and Martin boundary

  • Hans Föllmer
Seconde Partie: Exposes 1973/74
Part of the Lecture Notes in Mathematics book series (LNM, volume 465)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    DOBRUSHIN, R. L.: Description of a random field by means of conditional probabilities and conditions of its regularity. Theor. Probability Appl. 13, 197–224 (1968).CrossRefGoogle Scholar
  2. [2]
    DOBRUSHIN, R. L. and MINLOS, R. A.: Construction of a one-dimensional Quantum Field via a continuous Markov Field. To appear.Google Scholar
  3. [3]
    FUNFORD, N. and SCHWARTZ, J. T.: Linear Operators I. New York: Interscience 1958.Google Scholar
  4. [4]
    DYNKIN, E. B.: Entrance and Exit Spaces for a Markov Process. Actes, Congrès intern. Math., 1970. Tome 2, 507–512 (1971).Google Scholar
  5. [5]
    DYSON, F. J.: Existence of a phase-transition in a one dimensional Ising Ferromagnet. Comm. Math. Phys. 12, 91 (1969).MathSciNetCrossRefGoogle Scholar
  6. [6]
    FÖLLMER, H.: The Exit Measure of a Supermartingale. Z. Wahrscheinlichkeitstheorie verw. Geb. 21, 154–166 (1972).CrossRefGoogle Scholar
  7. [7]
    GEORGII, H.-O.: Two Remarks on Extremal Equilibrium States. Comm. Math. Phys. 32, 107–118 (1970).MathSciNetCrossRefGoogle Scholar
  8. [8]
    GUERRA, F., ROSEN, L., SIMON, B.: The P(ϕ)2 Euclidean Quantum Field Theory as Classical Statistical Mechanics. To appear.Google Scholar
  9. [9]
    MEYER, P. A.: Un lemme de théorie des martingales. Sém. Probabilités III. Lecture Notes Mathematics 88 (1969).Google Scholar
  10. [10]
    NELSON, E.: The Free Markoff Field. J. Functional Analysis 12, 211–227 (1973).MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    PARATHASARATHY, K. R.: Probability measures on metric spaces. New York-London: Academic Press 1967.Google Scholar
  12. [12]
    PRESTON, C. J.: Specification of random fields. To appear.Google Scholar
  13. [13]
    SIMON, B.: Positivity of the Hamiltonian Semigroup and the Construction of Euclidean Region Fields. To appear.Google Scholar
  14. [14]
    SPITZER, F.: Random fields and interacting particle systems. Notes on lectures given at the 1971 MAA Summer Seminar, Williams College, Williamstown, Mass. Mathematical Association of America 1971.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1975

Authors and Affiliations

  • Hans Föllmer

There are no affiliations available

Personalised recommendations