Applying monoid duality to a double contact process

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F23%3A00572568" target="_blank" >RIV/67985556:_____/23:00572568 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/23:10465394

Výsledek na webu

<a href="https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Applying-monoid-duality-to-a-double-contact-process/10.1214/23-EJP961.full" target="_blank" >https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Applying-monoid-duality-to-a-double-contact-process/10.1214/23-EJP961.full</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/23-EJP961" target="_blank" >10.1214/23-EJP961</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Applying monoid duality to a double contact process

Popis výsledku v původním jazyce

In this paper we use duality techniques to study a coupling of the well-known contact process (CP) and the annihilating branching process. As the latter can be seen as a cancellative version of the contact process, we rebrand it as the cancellative contact process (cCP). Our process of interest will consist of two components, the first being a CP and the second being a cCP. We call this process the double contact process (2CP) and prove that it has (depending on the model parameters) at most one invariant law under which ones are present in both processes. In particular, we can choose the model parameters in such a way that CP and cCP are monotonely coupled. In this case also the above mentioned invariant law will have the property that, under it, ones (modeling “infected individuals”) can only be present in the cCP at sites where there are also ones in the CP. Along the way we extend the dualities for Markov processes discovered in our paper “Commutative monoid duality” to processes on infinite state spaces so that they, in particular, can be used for interacting particle systems.

Název v anglickém jazyce

Applying monoid duality to a double contact process

Popis výsledku anglicky

In this paper we use duality techniques to study a coupling of the well-known contact process (CP) and the annihilating branching process. As the latter can be seen as a cancellative version of the contact process, we rebrand it as the cancellative contact process (cCP). Our process of interest will consist of two components, the first being a CP and the second being a cCP. We call this process the double contact process (2CP) and prove that it has (depending on the model parameters) at most one invariant law under which ones are present in both processes. In particular, we can choose the model parameters in such a way that CP and cCP are monotonely coupled. In this case also the above mentioned invariant law will have the property that, under it, ones (modeling “infected individuals”) can only be present in the cCP at sites where there are also ones in the CP. Along the way we extend the dualities for Markov processes discovered in our paper “Commutative monoid duality” to processes on infinite state spaces so that they, in particular, can be used for interacting particle systems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA20-08468S" target="_blank" >GA20-08468S: Limity interagujících stochastických modelů na velkých škálách</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

1083-6489

Svazek periodika

28

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

70

Kód UT WoS článku

001002487000001

EID výsledku v databázi Scopus

2-s2.0-85162844943