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

scholarly journals SOME INEQUALITIES FOR THEORETICAL SPATIAL ECOLOGY

2013 ◽  
Vol 55 (1) ◽  
pp. 55-68
Author(s):  
PAUL F. SLADE
Keyword(s):  
Statistical Mechanics ◽  
Spatial Ecology ◽  
Spatial Competition ◽  
Contact Process ◽  
Spatial Dimension ◽  
Upper Bounds ◽  
Central Moment ◽  
Pair Approximation ◽  
Moment Equations ◽  
Moment Closures

AbstractInequalities for spatial competition verify the pair approximation of statistical mechanics introduced to theoretical ecology by Matsuda, Satō and Iwasa, among others. Spatially continuous moment equations were introduced by Bolker and Pacala and use a similar assumption in derivation. In the present article, I prove upper bounds for the$k\mathrm{th} $central moment of occupied sites in the contact process of a single spatial dimension. This result shows why such moment closures are effective in spatial ecology.

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.

scholarly journals Super-Exponential Extinction Time of the Contact Process on Random Geometric Graphs

2017 ◽  
Vol 27 (2) ◽  
pp. 162-185 ◽  
Author(s):  
VAN HAO CAN
Keyword(s):  
Infection Rate ◽  
Contact Process ◽  
Upper Bounds ◽  
Geometric Graphs ◽  
Extinction Time ◽  
Lower And Upper Bounds ◽  
Random Geometric Graphs

In this paper we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connection radius tending to infinity. We obtain that for any infection rate λ > 0, the contact process on these graphs survives a time super-exponential in the number of vertices.

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