Invariant measures of mass migration processes

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Invariant measures of mass migration processes

Original language description

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.

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

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

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Volume of the periodical

21

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

52

Pages from-to

1-52

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-84997190838