Aarhus Universitets segl

Sharp phase transition for Cox percolation

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review


  • Christian Hirsch
  • Benedikt Jahnel, Technical University of Braunschweig, Weierstrass Institute for Applied Analysis and Stochastics
  • ,
  • Stephen Muirhead, University of Melbourne

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, satisfies a local boundedness condition and can be constructed from a discrete iid random field, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction that allows us to compare different notions of influence.

TidsskriftElectronic Communications in Probability
Sider (fra-til)1-13
StatusUdgivet - okt. 2022

Bibliografisk note

Funding Information:
†CH would like to acknowledge the financial support of the CogniGron research center and the Ubbo Emmius Funds (Univ. of Groningen). BJ was supported by the German Research Foundation under Germany’s Excellence Strategy MATH+: The Berlin Mathematics Research Center, EXC-2046/1 project ID: 390685689, and the Leibniz Association within the Leibniz Junior Research Group on Probabilistic Methods for Dynamic Communication Networks as part of the Leibniz Competition. SM was supported by the Australian Research Council (ARC) Discovery Early Career Researcher Award DE200101467.

Publisher Copyright:
© 2022, Institute of Mathematical Statistics. All rights reserved.

Se relationer på Aarhus Universitet Citationsformater

ID: 294663288