scholarly journals The survival probability of the high-dimensional contact process with random vertex weights on the oriented lattice

2019 ◽  
Vol 16 (1) ◽  
pp. 49
Author(s):  
Xiaofeng Xue
Keyword(s):  
Survival Probability ◽  
Contact Process ◽  
High Dimensional

Upper bounds for survival probability of the contact process

1991 ◽  
Vol 63 (1-2) ◽  
pp. 115-130 ◽  
Author(s):  
Makoto Katori ◽  
Norio Konno
Keyword(s):  
Survival Probability ◽  
Contact Process ◽  
Upper Bounds

ANALYTICITY OF SURVIVAL PROBABILITY FOR CONTACT PROCESS AROUND t = 0

2007 ◽  
Vol 05 (01) ◽  
pp. 67-76 ◽  
Author(s):  
VLADIMIR BELITSKY ◽  
YASUNARI HIGUCHI ◽  
NORIO KONNO ◽  
NOBUAKI SUGIMINE
Keyword(s):  
Phase Transition ◽  
Simple Model ◽  
Power Series ◽  
Series Expansion ◽  
Infection Rate ◽  
Survival Probability ◽  
Contact Process ◽  
Power Series Expansion ◽  
General Setting ◽  
One Dimension

The contact process is a simple model for the spread of epidemics with an infection rate λ and has become one of the most prominent models to show a phase transition even in one dimension. The transition is characterized by the behavior of its survival probability at time t, ρ(t). Clarifying how ρ(t) depends on λ and t is one of the interesting problems in studying the process. In the present paper, we show that the power series expansion of ρ(t) at t = 0 is entirely analytic. We also prove that the coefficients of this power series form an alternate sequence. To our knowledge, no result is known on the analyticity of ρ(t) in t = 0 except the first author's previous result in 1995. Our paper extends the result to a more general setting by using a different method.

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