scholarly journals Hydrodynamic limits for long-range asymmetric interacting particle systems

2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Sunder Sethuraman ◽  
Doron Shahar
Keyword(s):  
Long Range ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Hydrodynamic Limits ◽  
Interacting Particle

MARKOV SEMIGROUPS ON UHF ALGEBRAS

1993 ◽  
Vol 05 (03) ◽  
pp. 587-600 ◽  
Author(s):  
TAKU MATSUI
Keyword(s):  
Long Range ◽  
Interacting Particle Systems ◽  
Sufficient Conditions ◽  
Particle Systems ◽  
Unique Ergodicity ◽  
Markov Semigroups ◽  
Interacting Particle ◽  
Long Range Interactions

We consider a class of Markov semigroups on UHF algebras. We establish the existence of dynamics for long range interactions. Our idea is a non-commutative extension of the argument for classical interacting particle systems. As a by-product we obtain sufficient conditions for unique ergodicity.

scholarly journals Condensation of SIP Particles and Sticky Brownian Motion

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Self Duality ◽  
Inclusion Process ◽  
Interacting Particle ◽  
New Information ◽  
Homogeneous Product ◽  
Coarsening Dynamics ◽  
The Difference

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

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