About: Noninvadability implies noncoexistence for a class of cancellative systems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	Noninvadability implies noncoexistence for a class of cancellative systems Noninvadability implies noncoexistence for a class of cancellative systems (en)
skos:prefLabel	Noninvadability implies noncoexistence for a class of cancellative systems Noninvadability implies noncoexistence for a class of cancellative systems (en)
skos:notation	RIV/67985556:_____/13:00392519!RIV14-GA0-67985556
http://linked.open...avai/predkladatel	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP201/10/0752)
http://linked.open...iv/cisloPeriodika	38
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Swart, Jan M.
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	91940
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/13:00392519
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	cancellative system; interface tightness; duality; coexistence; Neuhauser-Pacala model; affine voter model; rebellious voter model; balancing selection; branching; annihilation; parity preservation (en)
http://linked.open.../riv/klicoveSlovo	duality branching annihilation balancing selection coexistence Neuhauser-Pacala model affine voter model cancellative system interface tightness parity preservation rebellious voter model
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[7BBA2A67F36E]
http://linked.open...i/riv/nazevZdroje	Electronic Communications in Probability
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Stochastic Space-Time Systems
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	18
http://linked.open...iv/tvurceVysledku	Swart, Jan M.
http://linked.open...ain/vavai/riv/wos	000319429300001
issn	1083-589X
number of pages	12 (xsd:int)
http://bibframe.org/vocab/doi	10.1214/ECP.v18-2471

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