Remarks on the FKG inequalities

1974 ◽  
Vol 36 (3) ◽  
pp. 227-231 ◽  
Author(s):  
Richard Holley
Keyword(s):  
Fkg Inequalities

A simple proof of certain FKG inequalities

1974 ◽  
Vol 15 (7) ◽  
pp. 998-999 ◽  
Author(s):  
James L. Monroe
Keyword(s):  
Simple Proof ◽  
Fkg Inequalities

A generalization of the FKG inequalities

1974 ◽  
Vol 36 (3) ◽  
pp. 233-241 ◽  
Author(s):  
C. J. Preston
Keyword(s):  
Fkg Inequalities

Brownian Survival in a Clusterized Trapping Medium

1998 ◽  
Vol 10 (02) ◽  
pp. 147-189 ◽  
Author(s):  
Sergio Albeverio ◽  
Leonid V. Bogachev
Keyword(s):  
Brownian Particle ◽  
Cluster Process ◽  
Poisson Cluster Process ◽  
Cluster Point Process ◽  
Long Time ◽  
Fkg Inequalities ◽  
Poisson Cluster ◽  
Random Traps ◽  
Physical Literature ◽  
Trapping Process

The survival problem for a Brownian particle moving among random traps is considered in the case where the traps are correlated in a particular fashion being gathered in clusters. It is assumed that the clusters are statistically identical and independent of each other and are distributed in space according to a Poisson law. Mathematically, such a trapping medium is described via a Poisson cluster point process. We prove that the particle survival probability is increased at all times as compared to the case of noncorrelated (Poissonian) traps, which implies the slowdown of the trapping process. It is shown that this effect may be interpreted as the manifestation of the trap "attraction", thus supporting assertions on the qualitative influence of the trap "interaction" on the trapping rate claimed earlier in the physical literature. The long-time survival asymptotics (of Donsker–Varadhan type) is also derived. By way of appendix, FKG inequalities for certain functionals are proven and the limiting distribution for a Poisson cluster process, under clusters' scaling, is determined.

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