Noninvadability implies noncoexistence for a class of cancellative systems

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Noninvadability implies noncoexistence for a class of cancellative systems

Original language 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-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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GAP201%2F10%2F0752" target="_blank" >GAP201/10/0752: Stochastic Space-Time Systems</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

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

Name of the periodical

Electronic Communications in Probability

ISSN

1083-589X

e-ISSN

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Volume of the periodical

18

Issue of the periodical within the volume

38

Country of publishing house

US - UNITED STATES

Number of pages

12

Pages from-to

1-12

UT code for WoS article

000319429300001

EID of the result in the Scopus database

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