We provide two methods to construct zero-range processes with superlinear rates on . In the first method these rates can grow very fast, if either the dynamics and the initial distribution are translation invariant or if only nearest neighbour translation invariant jumps are permitted, in the one-dimensional lattice. In the second method the rates cannot grow as fast but more general dynamics are allowed.
E. Andjel was partially supported first by CNPq grant 300722/2013-3 and then by FAPERJ grant E-26/200.033/2016. I. Armendáriz was partially funded by the PICT grant 2015 “Grafos aleatorios, procesos puntuales y metaestabilidad” and PIP grant PIP11220130100521CO. M. Jara was funded by ERC Horizon 2020 grant 715734, CNPq grant 305075/2017-9 and FAPERJ grant E-29/203.012/201. I. Armendáriz and M. Jara were partially supported by MathAmSud project “Random Structures and Processes in Statistical Mechanics”.
Dedicated to the memory of Thomas M. Liggett
The authors thank the referees for their careful reading and sharp suggestions. E. Andjel also thanks Maria Eulalia Vares for interesting discussions concerning the martingale problem and IMPA (Rio de Janeiro, Brazil) for its hospitality.
"Zero-range processes with rapidly growing rates." Electron. J. Probab. 26 1 - 29, 2021. https://doi.org/10.1214/21-EJP670