Results on the contact process with dynamic edges or under renewals

We analyze variants of the contact process that are built by modifying the percolative structure given by the graphical construction and develop a robust renormalization argument for proving extinction in such models. With this method, we obtain results on the phase diagram of two models: the Contact Process on Dynamic Edges introduced by Linker and Remenik and a generalization of the Renewal Contact Process introduced by Fontes, Marchetti, Mountford and Vares.

[1]  Daniel Remenik,et al.  The contact process with dynamic edges on $\mathbb {Z}$ , 2019, 1905.02641.

[2]  J. Steif.  A survey on dynamical percolation , 2009, 0901.4760.

[3]  Luiz Renato Fontes,et al.  Renewal Contact Processes: phase transition and survival , 2021 .

[4]  Daniel Remenik,et al.  The contact process in a dynamic random environment , 2008, 0901.2480.

[5]  Abel Klein,et al.  EXTINCTION OF CONTACT AND PERCOLATION PROCESSES IN A RANDOM ENVIRONMENT , 1994 .

[6]  H. Kesten.  Aspects of first passage percolation , 1986 .

[7]  Thomas M. Liggett,et al.  The Survival of One-Dimensional Contact Processes in Random Environments , 1992 .

[8]  École d'été de probabilités de Saint-Flour,et al.  École d'été de probabilités de Saint Flour XIV, 1984 , 1986 .

[9]  Ãgoston Pisztora,et al.  Surface order large deviations for Ising, Potts and percolation models , 1996 .

[10]  Pablo A. Gomes,et al.  Contact process under heavy-tailed renewals on finite graphs , 2019, Bernoulli.

[11]  Maury Bramson,et al.  The Contact Processes in a Random Environment , 1991 .

[12]  Jack Hanson,et al.  50 years of first passage percolation , 2015, 1511.03262.

[13]  A short proof of the phase transition for the vacant set of random interlacements , 2014, 1407.8460.

[14]  C. Newman,et al.  Persistent survival of one-dimensional contact processes in random environments , 1996 .

[15]  Daniel Valesin,et al.  Exponential rate for the contact process extinction time , 2021, Annales de la Faculté des sciences de Toulouse : Mathématiques.

[16]  R. Durrett.  Probability: Theory and Examples , 1993 .

[17]  M. Vares,et al.  Contact process under renewals I , 2018, Stochastic Processes and their Applications.

[18]  R. Doney,et al.  Local large deviations and the strong renewal theorem , 2016, Electronic Journal of Probability.

[19]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

[20]  R. Schonmann,et al.  Domination by product measures , 1997 .

[21]  Olivier Garet,et al.  Asymptotic shape for the contact process in random environment , 2009, 0910.1230.

[22]  Surface order large deviations for 2D FK-percolation and Potts models , 2003, math/0303117.

[23]  T. E. Harris.  Contact Interactions on a Lattice , 1974 .

[24]  G. Grimmett,et al.  The Critical Contact Process Dies Out , 1990 .

[25]  Stefan Grosskinsky Warwick,et al.  Interacting Particle Systems , 2016 .

[26]  A. Sznitman.  Decoupling inequalities and interlacement percolation on G×ℤ , 2010, 1010.1490.

[27]  T. E. Harris.  Additive Set-Valued Markov Processes and Graphical Methods , 1978 .

[28]  Enrique Andjel.  Survival of multidimensional contact process in random environments , 1992 .