scholarly journals Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Akira Sakai ◽  
Gordon Slade
Keyword(s):  
Contact Process ◽  
Oriented Percolation ◽  
High Dimensional ◽  
Spatial Moments ◽  
Lattice Trees ◽  
Process Oriented ◽  
Critical Contact

Super-Brownian Motion and Critical Spatial Stochastic Systems

2004 ◽  
Vol 47 (2) ◽  
pp. 280-297 ◽  
Author(s):  
Ed Perkins
Keyword(s):  
Brownian Motion ◽  
Limit Theorems ◽  
Stochastic Systems ◽  
Contact Process ◽  
Voter Model ◽  
Oriented Percolation ◽  
Short Introduction ◽  
Super Brownian Motion

AbstractThis article is a short introduction to super-Brownian motion. Some of its properties are discussed but our main objective is to describe a number of limit theorems which show super-Brownian motion is a universal limit for rescaled spatial stochastic systems at criticality above a critical dimenson. These systems include the voter model, the contact process and critical oriented percolation.

The critical contact process seen from the right edge

1991 ◽  
Vol 87 (3) ◽  
pp. 325-332 ◽  
Author(s):  
J. T. Cox ◽  
R. Durrett ◽  
R. Schinazi
Keyword(s):  
Contact Process ◽  
The Right ◽  
Critical Contact

scholarly journals Ageing in the critical contact process: a Monte Carlo study

2004 ◽  
Vol 37 (44) ◽  
pp. 10497-10512 ◽  
Author(s):  
José J Ramasco ◽  
Malte Henkel ◽  
Maria Augusta Santos ◽  
Constantino A da Silva Santos
Keyword(s):  
Monte Carlo ◽  
Contact Process ◽  
Monte Carlo Study ◽  
Critical Contact

Lattice trees and super-Brownian motion

1997 ◽  
Vol 40 (1) ◽  
pp. 19-38 ◽  
Author(s):  
Eric Derbez ◽  
Gordon Slade
Keyword(s):  
Brownian Motion ◽  
Mean Field Theory ◽  
Scaling Limit ◽  
Mean Field ◽  
High Dimensional ◽  
High Dimensions ◽  
Lace Expansion ◽  
Brownian Excursion ◽  
Lattice Trees ◽  
Super Brownian Motion

AbstractThis article discusses our recent proof that above eight dimensions the scaling limit of sufficiently spread-out lattice trees is the variant of super-Brownian motion calledintegrated super-Brownian excursion(ISE), as conjectured by Aldous. The same is true for nearest-neighbour lattice trees in sufficiently high dimensions. The proof, whose details will appear elsewhere, uses the lace expansion. Here, a related but simpler analysis is applied to show that the scaling limit of a mean-field theory is ISE, in all dimensions. A connection is drawn between ISE and certain generating functions and critical exponents, which may be useful for the study of high-dimensional percolation models at the critical point.

The critical contact process on a homogeneous tree

1994 ◽  
Vol 31 (1) ◽  
pp. 250-255 ◽  
Author(s):  
Gregory J. Morrow ◽  
Rinaldo B. Schinazi ◽  
Yu Zhang
Keyword(s):  
Contact Process ◽  
Homogeneous Tree ◽  
Expected Number ◽  
Critical Contact ◽  
Number Of Particles

We prove that the expected number of particles of the critical contact process on a homogeneous tree is bounded above. This is the first graph for which the behavior of the expected number of particles of the critical contact process is known. As an easy corollary of our result we get that the critical contact process dies out on any homogeneous tree. This completes the work of Pemantle (1992).

scholarly journals The Critical Contact Process Dies Out

1990 ◽  
Vol 18 (4) ◽  
pp. 1462-1482 ◽  
Author(s):  
Carol Bezuidenhout ◽  
Geoffrey Grimmett
Keyword(s):  
Contact Process ◽  
Critical Contact
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