scholarly journals Equilibration in the Kac Model Using the GTW Metric $$d_2$$

2017 ◽  
Vol 169 (1) ◽  
pp. 168-186
Author(s):  
H. Tossounian
Keyword(s):  
Kac Model

scholarly journals On a Thermostated Kac Model with Rescaling

2021 ◽  
Author(s):  
Roberto Cortez ◽  
Hagop Tossounian
Keyword(s):  
Kac Model

scholarly journals Convergence of the Two-Dimensional Dynamic Ising-Kac Model to Φ24

2016 ◽  
Vol 70 (4) ◽  
pp. 717-812 ◽  
Author(s):  
Jean-Christophe Mourrat ◽  
Hendrik Weber
Keyword(s):  
Two Dimensional ◽  
Kac Model

scholarly journals A Kac Model for Kinetic Annihilation

2020 ◽  
Vol 30 (4) ◽  
pp. 1455-1501
Author(s):  
Bertrand Lods ◽  
Alessia Nota ◽  
Federica Pezzotti
Keyword(s):  
Kac Model

scholarly journals KINETIC LIMITS FOR PAIR-INTERACTION DRIVEN MASTER EQUATIONS AND BIOLOGICAL SWARM MODELS

2013 ◽  
Vol 23 (07) ◽  
pp. 1339-1376 ◽  
Author(s):  
ERIC CARLEN ◽  
PIERRE DEGOND ◽  
BERNT WENNBERG
Keyword(s):  
Kinetic Theory ◽  
Particle System ◽  
Pair Interaction ◽  
Master Equations ◽  
Propagation Of Chaos ◽  
Invariant Density ◽  
Homogeneous Case ◽  
Kac Model ◽  
Spatially Homogeneous ◽  
Definition Of

We consider a class of stochastic processes modeling binary interactions in an N-particle system. Examples of such systems can be found in the modeling of biological swarms. They lead to the definition of a class of master equations that we call pair-interaction driven master equations. In the spatially homogeneous case, we prove a propagation of chaos result for this class of master equations which generalizes Mark Kac's well-known result for the Kac model in kinetic theory. We use this result to study kinetic limits for two biological swarm models. We show that propagation of chaos may be lost at large times and we exhibit an example where the invariant density is not chaotic.

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