STOCHASTIC COMPARISON OF POINT RANDOM FIELDS

We give an alternative proof of a point-process version of the FKG-Holley-Preston inequality which provides a sufficient condition for stochastic domination of probability measures, and for positive correlations of increasing functions.

[1]  M. Penrose On a continuum percolation model , 1991, Advances in Applied Probability.

[2]  C. J. Preston,et al.  A generalization of the FKG inequalities , 1974 .

[3]  Olle Häggström,et al.  Phase transition in continuum Potts models , 1996 .

[4]  S. Janson Bounds on the distributions of extremal values of a scanning process , 1984 .

[5]  C. Preston Spatial birth and death processes , 1975, Advances in Applied Probability.

[6]  T. Lindvall Lectures on the Coupling Method , 1992 .

[7]  C. Batty,et al.  Generalised Holley-Preston inequalities on measure spaces and their products , 1980 .

[8]  T. E. Harris A lower bound for the critical probability in a certain percolation process , 1960, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  A. Baddeley,et al.  Area-interaction point processes , 1993 .

[10]  D. Ruelle Statistical Mechanics: Rigorous Results , 1999 .

[11]  J. Lebowitz,et al.  Inequalities for higher order Ising spins and for continuum fluids , 1972 .

[12]  R. Holley Remarks on the FKG inequalities , 1974 .

[13]  Jennifer Chayes,et al.  The analysis of the Widom-Rowlinson model by stochastic geometric methods , 1995 .

[14]  John S. Rowlinson,et al.  New Model for the Study of Liquid–Vapor Phase Transitions , 1970 .

[15]  Walter Warmuth,et al.  Bemerkungen zu einer Arbeit von NGUYEN XUAN XANH und HANS ZESSIN , 1979 .

[16]  C. Fortuin,et al.  Correlation inequalities on some partially ordered sets , 1971 .