scholarly journals Interacting particle systems with long-range interactions: scaling limits and kinetic equations

2021 ◽  
Vol 32 (2) ◽  
pp. 335-377
Author(s):  
Alessia Nota ◽  
Juan Velázquez ◽  
Raphael Winter
Keyword(s):  
Long Range ◽  
Interacting Particle Systems ◽  
Kinetic Equations ◽  
Particle Systems ◽  
Scaling Limits ◽  
Interacting Particle ◽  
Long Range Interactions

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.

Diffusive Scaling Limits of Mutually Interacting Particle Systems

2004 ◽  
Vol 35 (6) ◽  
pp. 1512-1533
Author(s):  
Shui Feng ◽  
Ilie Grigorescu ◽  
Jeremy Quastel
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Scaling Limits ◽  
Interacting Particle
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