Equilibrium interfaces of biased voter models

0506795 - ÚTIA 2020 RIV US eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA16-15238S
Institutional support: RVO:67985556
Keywords : biased voter model * interface tightness * branching and coalescing random walks
OECD category: Pure mathematics
Impact factor: 1.537, year: 2019
Method of publishing: Limited access
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.
Permanent Link: http://hdl.handle.net/11104/0297991