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.

NONLINEAR PROBLEMS IN INFINITE INTERACTING PARTICLE SYSTEMS

2008 ◽  
Vol 11 (02) ◽  
pp. 179-211 ◽  
Author(s):  
ROBERT OLKIEWICZ ◽  
LIHU XU ◽  
BOGUSŁAW ZEGARLIŃSKI
Keyword(s):  
Configuration Space ◽  
Interacting Particle Systems ◽  
Nonlinear Problems ◽  
Particle Systems ◽  
Markov Semigroups ◽  
Infinite Dimensional ◽  
Interacting Particle

We introduce and study a class of nonlinear jump type Markov semigroups for systems with infinite dimensional configuration space.

A CLASS OF INTERACTING PARTICLE SYSTEMS ON THE INFINITE CYLINDER WITH FLOCKING PHENOMENA

2012 ◽  
Vol 22 (07) ◽  
pp. 1250008 ◽  
Author(s):  
SEUNG-YEAL HA ◽  
MOON-JIN KANG ◽  
CORRADO LATTANZIO ◽  
BRUNO RUBINO
Keyword(s):  
Numerical Simulation ◽  
Interacting Particle Systems ◽  
Sufficient Conditions ◽  
Particle Systems ◽  
Kuramoto Model ◽  
Infinite Cylinder ◽  
Interacting Particle ◽  
Proposed Model ◽  
Simulation Results ◽  
Flocking Motion

We present a class of extended Kuramoto models describing a flocking motion of particles on the infinite cylinder and provide sufficient conditions for the asymptotic formation of locked solutions where the distance between particles remains constant. Our proposed model includes the complex Kuramoto model for synchronization. We also provide several numerical simulation results and compare them with analytical results.

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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