Invariant measures of mass migration processes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F16%3A00464455" target="_blank" >RIV/67985556:_____/16:00464455 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1214/16-EJP4399" target="_blank" >http://dx.doi.org/10.1214/16-EJP4399</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/16-EJP4399" target="_blank" >10.1214/16-EJP4399</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Invariant measures of mass migration processes

Popis výsledku v původním jazyce

We introduce the “mass migration process (MMP), a conservative particle system on NZdNZd. It consists in jumps of kk particles (k1k1) between sites, with a jump rate depending only on the state of the system at the departure and arrival sites of the jump. It generalizes misanthropes processes, hence zero range and target processes. After the construction of MMP, our main focus is on its invariant measures. We derive necessary and sufficient conditions for the existence of translation invariant and invariant product probability measures. In the particular cases of asymmetric mass migration zero range and mass migration target dynamics, these conditions yield explicit solutions. If these processes are moreover attractive, we obtain a full characterization of all translation invariant, invariant probability measures. We also consider attractiveness properties (through couplings), condensation phenomena, and their links for MMP. We illustrate our results on many examples; we prove the coexistence of condensation and attractiveness in one of them.

Název v anglickém jazyce

Invariant measures of mass migration processes

Popis výsledku anglicky

We introduce the “mass migration process (MMP), a conservative particle system on NZdNZd. It consists in jumps of kk particles (k1k1) between sites, with a jump rate depending only on the state of the system at the departure and arrival sites of the jump. It generalizes misanthropes processes, hence zero range and target processes. After the construction of MMP, our main focus is on its invariant measures. We derive necessary and sufficient conditions for the existence of translation invariant and invariant product probability measures. In the particular cases of asymmetric mass migration zero range and mass migration target dynamics, these conditions yield explicit solutions. If these processes are moreover attractive, we obtain a full characterization of all translation invariant, invariant probability measures. We also consider attractiveness properties (through couplings), condensation phenomena, and their links for MMP. We illustrate our results on many examples; we prove the coexistence of condensation and attractiveness in one of them.

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

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

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

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Svazek periodika

21

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

52

Strana od-do

1-52

Kód UT WoS článku

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EID výsledku v databázi Scopus

2-s2.0-84997190838