Počet záznamů: 1  

A simple proof of exponential decay of subcritical contact processes

  1. 1.
    0462694 - UTIA-B 2019 RIV DE eng J - Článek v odborném periodiku
    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
    Grant CEP: GA ČR(CZ) GA16-15238S
    Institucionální podpora: RVO:67985556
    Klíčová slova: subcritical contact process * sharpness of the phase transition * eigenmeasure
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Pure mathematics
    Impakt faktor: 2.448, rok: 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.
    Trvalý link: http://hdl.handle.net/11104/0262360