WIAS Preprint No. 2922, (2022)
Sharp phase transition for Cox percolation
- Hirsch, Christian
- Jahnel, Benedikt
- Muirhead, Stephen
2020 Mathematics Subject Classification
- 60F10 60K35
- Cox point process, OSSS inequality, continuum percolation, Poisson point process, random environment, Delaunay tessellation
We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence and satisfies a local boundedness condition, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction.
- Electron. Comm. Probab., 27 (2022), pp. 48/1--48/13, DOI 10.1214/22-ECP487 .