0464455 20240111140926.820161027235959.9 84997190838 000396611400019 10.1214/16-EJP4399 52 s. E cav_un_epca*00419541083-6489211 (2016)1-52Institute of Mathematical Statistics interacting particle systems product invariant measures zero range process target process mass migration process condensation cav_un_auth*0101081 Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics Fajfrová Lucie UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0336114 Gobron T. FR cav_un_auth*0278702 Saada E. FR PDF http://library.utia.cas.cz/separaty/2016/SI/fajfrova-0464455.pdf cav_un_auth*0291241 GAP201/12/2613 GA ČR cav_un_auth*0334217 GA16-15238S GA ČR CZ 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. BA 2017 3 4 A hod 4ah 20231122141953.0 RVO:67985556 http://hdl.handle.net/11104/0263948 cav_un_auth*0332322 Université de Cergy-Pontoise FR cav_un_auth*0300547 Université Paris Descartes FR 1 Department of Stochastic Informatics UTIA-B 10103 STATISTICS & PROBABILITY S 60 2 Article Statistics Probability STATISTICS&PROBABILITY 1.040 0.073 6 0.01046 1.315 1163 1.792 Q1 0.865 41 Q3 68.522 45.6 Q2 Q1 45.565 2016 Soubory v repozitáři: fajfrova-0464455.pdf 84997190838 SCOPUS 000396611400019 WOS PDF cav_un_epca*0041954 Electronic Journal of Probability 1083-6489 1083-6489 Roč. 21 č. 1 2016 1 52 Institute of Mathematical Statistics