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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 


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;

2National University; School of Mathematics; Heredia; Costa Rica;


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.


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


C, Bernardin; P, Gonçalves; B, Jiménez-Oviedo. Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps, Markov Processes and Related Fields 25(2017), no. 2, 217- 274. documentLinks ]

C, Bernardin; P, Gonçalves; B, Jiménez-Oviedo. A microscopic model for a one parameter class of fractional Laplacians with Dirichlet boundary conditions. Archive for Rational Mechanics and Analysis, (2020) 1-48. Doi: 10.1007/s00205-020-01549-9 [ Links ]

C, Bernardin; B, Jiménez-Oviedo. Fractional Fick’s law for the boundary driven exclusion process with long jumps, Latin American Journal of Probability and Mathematical Statistics 14(2016), no. 1, 473-501. Doi: 10. 30757/ALEA.v14-25 [ Links ]

P, Billingsley. Convergence of Probability Measures, John Wiley & Sons, New York, 2013. [ Links ]

Q, Guan; Z, Ma. Reflected symmetric α-stable processes and regional fractional Laplacian, Probability theory and related fields, Springer 134(2005), no. 4, 649-694. Doi: 10.1007/s00440-005-0438-3 [ Links ]

C, Mou; Y, Yi. Interior regularity for regional fractional Laplacian, Communications in Mathematical Physics, Springer 340(2015), no. 1, 233-251. Doi: 10.1007/s00220-015-2445-2 [ Links ]

J, Vázquez. Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators, Discrete and Continuous Dynamical Systems - Series S 7(2014), no. 4, 857-885. Doi: 10.3934/dcdss.2014.7. 857 [ Links ]

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