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Noninvadability implies noncoexistence for a class of cancellative systems

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Noninvadability implies noncoexistence for a class of cancellative systems
2.	Creator	Author's name, affiliation, country	Jan M. Swart; Institute of Information Theory and Automation of the ASCR (UTIA); Czech Republic
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Cancellative system ; interface tightness ; duality, coexistence ; Neuhauser-Pacala model ; affine voter model ; rebellious voter model ; balancing selection ; branching ; annihilation ; parity preservation
3.	Subject	Subject classification	Primary: 82C22; Secondary: 60K35, 92D25, 82C24
4.	Description	Abstract	There exist a number of results proving that for certain classes of interacting particle systems in population genetics, mutual invadability of types implies coexistence. In this paper we prove a sort of converse statement for a class of one-dimensional cancellative systems that are used to model balancing selection. We say that a model exhibits strong interface tightness if started from a configuration where to the left of the origin all sites are of one type and to the right of the origin all sites are of the other type, the configuration as seen from the interface has an invariant law in which the number of sites where both types meet has finite expectation. We prove that this implies noncoexistence, i.e., all invariant laws of the process are concentrated on the constant configurations. The proof is based on special relations between dual and interface models that hold for a large class of one-dimensional cancellative systems and that are proved here for the first time.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Work sponsored by GAČR grant: P201/10/0752.
7.	Date	(YYYY-MM-DD)	2013-05-23
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/2471
10.	Identifier	Digital Object Identifier	10.1214/ECP.v18-2471
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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