Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models

1996 ◽  
pp. 42-95 ◽  
Author(s):  
Sylvie Méléard
Keyword(s):  
Asymptotic Behaviour ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Interacting Particle

Estimation of critical values in interacting particle systems

2000 ◽  
Vol 37 (01) ◽  
pp. 118-125
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Gerardo Sanz
Keyword(s):  
Computer Simulation ◽  
Asymptotic Behaviour ◽  
Interacting Particle Systems ◽  
Particle System ◽  
Particle Systems ◽  
Critical Values ◽  
Interacting Particle System ◽  
Absorption Time ◽  
Interacting Particle ◽  
Absorbing State

The estimation of critical values is one of the most interesting problems in the study of interacting particle systems. The bounds obtained analytically are not usually very tight and, therefore, computer simulation has been proved to be very useful in the estimation of these values. In this paper we present a new method for the estimation of critical values in any interacting particle system with an absorbing state. The method, based on the asymptotic behaviour of the absorption time of the process, is very easy to implement and provides good estimates. It can also be applied to processes different from particle systems.

Estimation of critical values in interacting particle systems

2000 ◽  
Vol 37 (1) ◽  
pp. 118-125
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Gerardo Sanz
Keyword(s):  
Computer Simulation ◽  
Asymptotic Behaviour ◽  
Interacting Particle Systems ◽  
Particle System ◽  
Particle Systems ◽  
Critical Values ◽  
Interacting Particle System ◽  
Absorption Time ◽  
Interacting Particle ◽  
Absorbing State

The estimation of critical values is one of the most interesting problems in the study of interacting particle systems. The bounds obtained analytically are not usually very tight and, therefore, computer simulation has been proved to be very useful in the estimation of these values. In this paper we present a new method for the estimation of critical values in any interacting particle system with an absorbing state. The method, based on the asymptotic behaviour of the absorption time of the process, is very easy to implement and provides good estimates. It can also be applied to processes different from particle systems.

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.

scholarly journals Holomorphic Bogoliubov functionals for interacting particle systems in continuum

2006 ◽  
Vol 238 (2) ◽  
pp. 375-404 ◽  
Author(s):  
Yuri G. Kondratiev ◽  
Tobias Kuna ◽  
Maria João Oliveira
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Interacting Particle
Sign in / Sign up

Export Citation Format

Share Document