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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.28 n.1 San José Jan./Jul. 2021

http://dx.doi.org/10.15517/rmta.v28i1.36294 

Artículo

Hydrostatic limit for the symmetric exclusion process with long jumps: supper-diffusive case

Límite hidroestático para el proceso de exclusión con saltos largos: caso super-difusivo

Byron Jiménez Oviedo1 

Jeremías Ramírez Jiménez2 

1National University; School of Mathematics; Heredia; Costa Rica; byron.jimenez.oviedo@una.ac.cr

2National University; School of Mathematics; Heredia; Costa Rica; jeremias.ramirez.jimenez@una.ac.cr

Abstract

Hydrostatic behavior for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities are derived. The jump rate is described by a transition probability p which is proportional to | · |−(γ+1) for 1 < γ < 2 (supper-diffusive case). The reservoirs add or remove particles with rate proportional to κ > 0.

Keywords: exclusion process with long jumps; super-diffusion; fractional Fick’s law.

Resumen

Se deriva el comportamiento hidroestático del proceso de exclusión simple con saltos largos en contacto con depósitos infinitos con diferentes densidades. La tasa de salto es descrita por una función de probabilidad p que es proporcional a | · |−(γ+1) para 1 < γ < 2 (caso súperdifusivo). Los depósitos de partículas añaden o retiran partículas con una tasa propocional a κ > 0.

Palabras clave: proceso de exclusión con salto largos; super-difusión; ley de Fick fraccionaria.

Mathematics Subject Classification: 82C22, 60K35, 34A08.

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Acknowledgements

The author B. Jiménez is very grateful to Cédric Bernardin and Patrícia Gonçalves for useful teachings and discussions.

References

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Received: June 28, 2019; Revised: November 04, 2020; Accepted: October 30, 2020

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License