Equilibrium interfaces of biased voter models

0506795 - ÚTIA 2020 RIV US eng J - Článek v odborném periodiku
Sun, R. - Swart, Jan M. - Yu, J.
Equilibrium interfaces of biased voter models.
Annals of Applied Probability. Roč. 29, č. 4 (2019), s. 2556-2593. ISSN 1050-5164
Grant CEP: GA ČR(CZ) GA16-15238S
Institucionální podpora: RVO:67985556
Klíčová slova: biased voter model * interface tightness * branching and coalescing random walks
Obor OECD: Pure mathematics
Impakt faktor: 1.537, rok: 2019
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2019/SI/swart-0506795.pdf https://projecteuclid.org/euclid.aoap/1563869050

A one-dimensional interacting particle system is said to exhibit interface tightness if starting in an initial condition describing the interface between two constant configurations of different types, the process modulo translations is positive recurrent. In a biological setting, this describes two populations that do not mix, and it is believed to be a common phenomenon in one-dimensional particle systems. Interface tightness has been proved for voter models satisfying a finite second moment condition on the rates. We extend this to biased voter models. Furthermore, we show that the distribution of the equilibrium interface for the biased voter model converges to that of the voter model when the bias parameter tends to zero. A key ingredient is an identity for the expected number of boundaries in the equilibrium voter model interface, which is of independent interest.
Trvalý link: http://hdl.handle.net/11104/0297991