Noninvadability implies noncoexistence for a class of cancellative systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F13%3A00392519" target="_blank" >RIV/67985556:_____/13:00392519 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1214/ECP.v18-2471" target="_blank" >http://dx.doi.org/10.1214/ECP.v18-2471</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/ECP.v18-2471" target="_blank" >10.1214/ECP.v18-2471</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Noninvadability implies noncoexistence for a class of cancellative systems

Popis výsledku v původním jazyce

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-dimensionalcancellative 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.

Název v anglickém jazyce

Noninvadability implies noncoexistence for a class of cancellative systems

Popis výsledku anglicky

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-dimensionalcancellative 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F10%2F0752" target="_blank" >GAP201/10/0752: Stochastické časoprostorové systémy</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Communications in Probability

ISSN

1083-589X

e-ISSN

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Svazek periodika

18

Číslo periodika v rámci svazku

38

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

1-12

Kód UT WoS článku

000319429300001

EID výsledku v databázi Scopus

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