A simple proof of exponential decay of subcritical contact processes

0462694 - ÚTIA 2019 RIV DE eng J - Journal Article
Swart, Jan M.
A simple proof of exponential decay of subcritical contact processes.
Probability Theory and Related Fields. Roč. 170, 1-2 (2018), s. 1-9. ISSN 0178-8051. E-ISSN 1432-2064
R&D Projects: GA ČR(CZ) GA16-15238S
Institutional support: RVO:67985556
Keywords : subcritical contact process * sharpness of the phase transition * eigenmeasure
OECD category: Pure mathematics
Impact factor: 2.448, year: 2018
http://library.utia.cas.cz/separaty/2016/SI/swart-0462694.pdf

This paper gives a new, simple proof of the known fact that for contact processes on general lattices, in the subcritical regime the expected number of infected sites decays exponentially fast as time tends to infinity. The proof also yields an explicit bound on the survival probability below the critical recovery rate, which shows that the critical exponent associated with this function is bounded from below by its mean-field value. The main idea of the proof is that if the expected number of infected sites decays slower than exponentially, then this implies the existence of a harmonic function that can be used to show that the process survives for any lower value of the recovery rate.
Permanent Link: http://hdl.handle.net/11104/0262360