Propagation of chaos for topological interactions

We consider a $N$-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit $N \to \infty$, as following from the previous analysis in [A. Blanchet, P. Degond, Topological interactions in a Boltzmann-type framework, J. Stat. Phys., 163 (2016), pp. 41-60.] can be rigorously derived. This means that the statistical independence (propagation of chaos) is indeed recovered in the limit, provided it is assumed at time zero.

• Publication year

  2018

• Venue

  The Annals of Applied Probability

• Publication date

  2018-03-05

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1214/19-AAP1469arXiv 1803.01922
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Kinetic Models for Topological Nearest-Neighbor Interactions

  2017cited by this paper
• On the Size of Chaos in the Mean Field Dynamics

  2017cited by this paper
• McKean–Vlasov limit for interacting systems with simultaneous jumps

  2017cited by this paper
• Synchronization of multi-agent systems with metric-topological interactions.

  2016cited by this paper
• One-sided convergence in the Boltzmann-Grad limit

  2016cited by this paper
• Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces

  2015cited by this paper
• Topological Interactions in a Boltzmann-Type Framework

  2015influential reference
• Emergence of the scale-invariant proportion in a flock from the metric-topological interaction

  2014cited by this paper
• The Boltzmann–Grad limit of a hard sphere system: analysis of the correlation error

  2014cited by this paper
• Consensus reaching in swarms ruled by a hybrid metric-topological distance

  2014cited by this paper
• Influence of the number of topologically interacting neighbors on swarm dynamics

  2014cited by this paper
• Flocking dynamics and mean-field limit in the Cucker–Smale-type model with topological interactions

  2013cited by this paper
• Multi-agent flocking under topological interactions

  2013cited by this paper
• A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

  2013cited by this paper
• On the validity of the Boltzmann equation for short range potentials

  2013cited by this paper
• From Newton to Boltzmann: Hard Spheres and Short-range Potentials

  2012cited by this paper
• Spatially balanced topological interaction grants optimal cohesion in flocking models

  2012cited by this paper
• Limited interactions in flocks: relating model simulations to empirical data

  2011cited by this paper
• Kac’s program in kinetic theory

  2011cited by this paper
• A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

  2011cited by this paper
• Particles approximations of Vlasov equations with singular forces : Propagation of chaos

  2011cited by this paper
• Some Causes of the Variable Shape of Flocks of Birds

  2011cited by this paper
• Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming

  2010cited by this paper
• Relevance of metric-free interactions in flocking phenomena.

  2010cited by this paper
• Multi-grid simulation of pedestrian counter flow with topological interaction

  2010cited by this paper
• FROM EMPIRICAL DATA TO INTER-INDIVIDUAL INTERACTIONS: UNVEILING THE RULES OF COLLECTIVE ANIMAL BEHAVIOR

  2010cited by this paper
• Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study

  2007cited by this paper
• Stochastic Numerics for the Boltzmann Equation

  2005cited by this paper
• Presented by :

  2004cited by this paper
• The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem

  2001cited by this paper
• Stationary particle systems approximating stationary solutions to the Boltzmann equation

  1998cited by this paper
• Stochastic particle approximations for generalized Boltzmann models and convergence estimates

  1997cited by this paper
• On some large systems of random particles which approximate scalar conservation laws

  1995cited by this paper
• Convergence of particle schemes for the Boltzmann equation

  1994cited by this paper
• The mathematical theory of dilute gases

  1994cited by this paper
• Topics in propagation of chaos

  1991cited by this paper
• A stochastic system of particles modelling the Euler equations

  1990cited by this paper
• Global validity of the Boltzmann equation for two- and three-dimensional rare gas in vacuum: Erratum and improved result

  1989cited by this paper
• Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum

  1986cited by this paper
• Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum

  1986cited by this paper
• The grad limit for a system of soft spheres

  1983cited by this paper
• The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles

  1977cited by this paper
• Time evolution of large classical systems

  1975cited by this paper
• Die Approximation der Lösung von Integro-Differentialgleichungen durch endliche Punktmengen

  1974cited by this paper
• The Vlasov equations

  1965cited by this paper
• Probability and Related Topics in Physical Sciences

  1960cited by this paper
• Foundations of Kinetic Theory

  1956cited by this paper

• Numerical Modeling of Flocking Dynamics with Topological Interactions

  2025cites this paper
• Cumulant Expansions of Groups of Operators for Particle Systems with Topological Nearest-neighbor Interaction

  2025cites this paper
• From microscopic to macroscopic: the large number dynamics of agents and cells, possibly interacting with a chemical background

  2024cites this paper
• Kinetic Theory of Self-Propelled Particles with Nematic Alignment

  2024cites this paper
• Kinetic description of swarming dynamics with topological interaction and emergent leaders

  2023cites this paper
• Propagation of chaos and hydrodynamic description for topological models

  2023cites this paper
• Propagation of chaos for topological interactions by a coupling technique

  2022influential citation
• Optimized leaders strategies for crowd evacuation in unknown environments with multiple exits

  2021cites this paper
• Modeling limited attention in opinion dynamics by topological interactions

  2020cites this paper
• Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

  2020cites this paper
• TOPOLOGICAL INTERACTIONS FOR COLLECTIVE DYNAMICS: A STUDY OF A (NOT SO) SIMPLE MODEL

  2019influential citation
• Some aspects of the inertial spin model for flocks and related kinetic equations

  2019cites this paper