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).

The critical contact process on a homogeneous tree

1994 ◽  
Vol 31 (01) ◽  
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).

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

scholarly journals Model biological population by branching processes

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Antoanela Terzieva
Keyword(s):  
Population Dynamics ◽  
Cell Division ◽  
Stochastic Processes ◽  
End Of Life ◽  
Branching Processes ◽  
Expected Number ◽  
Biological Population ◽  
Different Types ◽  
Unicellular Organisms ◽  
Number Of Particles

Consider a population of two or more different types of cells that at the end of life create two new cells through cell division. We model the population dynamics using a multitype branching stochastic processes. Under consideration are processes of Bieneme-Galton-Watson and of Bellman-Harris for the Markovian case.   drawn Conclusions about the expected number of particles of each type after a random time are drawn. The proposed models could be applicable not only for populations of a unicellular organisms, but also for sets of objects which operate a certain period of time and then split into two new objects or change their type.

scholarly journals Quantum Techniques for Reaction Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
John C. Baez
Keyword(s):  
Master Equation ◽  
Rate Equation ◽  
Quantum Physics ◽  
Time Derivative ◽  
Reaction Network ◽  
Reaction Networks ◽  
Expected Number ◽  
Second Quantization ◽  
Stochastic Time ◽  
Number Of Particles

Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar purposes in computer science and biology. As noted by Doi and others, techniques from quantum physics, such as second quantization, can be adapted to apply to such systems. Here we use these techniques to study how the “master equation” describing stochastic time evolution for a reaction network is related to the “rate equation” describing the deterministic evolution of the expected number of particles of each species in the large-number limit. We show that the relation is especially strong when a solution of master equation is a “coherent state”, meaning that the numbers of entities of each kind are described by independent Poisson distributions. Remarkably, in this case the rate equation and master equation give the exact same formula for the time derivative of the expected number of particles of each species.

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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