Stochastic growth models: bounds on critical values

1992 ◽  
Vol 29 (1) ◽  
pp. 11-20 ◽  
Author(s):  
R. Durrett
Keyword(s):  
Interacting Particle Systems ◽  
Growth Models ◽  
Upper Bounds ◽  
Particle Systems ◽  
Critical Values ◽  
Oriented Percolation ◽  
Finite Sets ◽  
Stochastic Growth ◽  
Interacting Particle ◽  
Stochastic Growth Models

We give upper bounds on the critical values for oriented percolation and some interacting particle systems by computing their behavior on small finite sets.

Stochastic growth models: bounds on critical values

1992 ◽  
Vol 29 (01) ◽  
pp. 11-20 ◽  
Author(s):  
R. Durrett
Keyword(s):  
Interacting Particle Systems ◽  
Growth Models ◽  
Upper Bounds ◽  
Particle Systems ◽  
Critical Values ◽  
Oriented Percolation ◽  
Finite Sets ◽  
Stochastic Growth ◽  
Interacting Particle ◽  
Stochastic Growth Models

We give upper bounds on the critical values for oriented percolation and some interacting particle systems by computing their behavior on small finite sets.

Estimating the critical values of stochastic growth models

1993 ◽  
Vol 30 (2) ◽  
pp. 455-461 ◽  
Author(s):  
L. Buttell ◽  
J. T. Cox ◽  
R. Durrett
Keyword(s):  
Interacting Particle Systems ◽  
Growth Models ◽  
Computer Time ◽  
Particle Systems ◽  
Critical Values ◽  
Stochastic Growth ◽  
Interacting Particle ◽  
Stochastic Growth Models

Interacting particle systems provide an attractive framework for modelling the growth and spread of biological populations and diseases. One problem with their use in applications is that in most cases the existing information about their critical values and equilibrium densities is too crude to be useful. In this paper we describe a method for estimating these quantities that does not require very much computer time and produces fairly accurate results.

Estimating the critical values of stochastic growth models

1993 ◽  
Vol 30 (02) ◽  
pp. 455-461
Author(s):  
L. Buttell ◽  
J. T. Cox ◽  
R. Durrett
Keyword(s):  
Interacting Particle Systems ◽  
Growth Models ◽  
Computer Time ◽  
Particle Systems ◽  
Critical Values ◽  
Stochastic Growth ◽  
Interacting Particle ◽  
Stochastic Growth Models

Interacting particle systems provide an attractive framework for modelling the growth and spread of biological populations and diseases. One problem with their use in applications is that in most cases the existing information about their critical values and equilibrium densities is too crude to be useful. In this paper we describe a method for estimating these quantities that does not require very much computer time and produces fairly accurate results.

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.

scholarly journals Heat kernel upper bounds for interacting particle systems

2019 ◽  
Vol 47 (2) ◽  
pp. 1056-1095
Author(s):  
Arianna Giunti ◽  
Yu Gu ◽  
Jean-Christophe Mourrat
Keyword(s):  
Heat Kernel ◽  
Interacting Particle Systems ◽  
Upper Bounds ◽  
Particle Systems ◽  
Interacting Particle

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.

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