Invariant measures of mass migration processes

0464455 - ÚTIA 2017 RIV US eng J - Článek v odborném periodiku
Fajfrová, Lucie - Gobron, T. - Saada, E.
Invariant measures of mass migration processes.
Electronic Journal of Probability. Roč. 21, č. 1 (2016), s. 1-52, č. článku 60. ISSN 1083-6489. E-ISSN 1083-6489
Grant CEP: GA ČR GAP201/12/2613; GA ČR(CZ) GA16-15238S
Institucionální podpora: RVO:67985556
Klíčová slova: interacting particle systems * product invariant measures * zero range process * target process * mass migration process * condensation
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.904, rok: 2016
http://library.utia.cas.cz/separaty/2016/SI/fajfrova-0464455.pdf

We introduce the “mass migration process” (MMP), a conservative particle system on NZdNZd. It consists in jumps of kk particles (k≥1k≥1) 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.
Trvalý link: http://hdl.handle.net/11104/0263948