Quenched asymptotics for interacting diffusions on inhomogeneous random graphs
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Publication:2229562
DOI10.1016/j.spa.2020.06.010zbMath1454.60046arXiv1811.09229OpenAlexW2901173480MaRDI QIDQ2229562
Publication date: 18 February 2021
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1811.09229
random graphsinteracting diffusionsgraph convergencemean-field systemsneural field equationspatially-extended systems
Random graphs (graph-theoretic aspects) (05C80) Strong limit theorems (60F15) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Fokker-Planck equations (35Q84)
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A note on Fokker-Planck equations and graphons ⋮ Stationarity and uniform in time convergence for the graphon particle system ⋮ Multivariate Hawkes processes on inhomogeneous random graphs ⋮ Marginal dynamics of interacting diffusions on unimodular Galton-Watson trees ⋮ A numerical method for a nonlocal diffusion equation with additive noise ⋮ Graphon particle system: uniform-in-time concentration bounds ⋮ The Kuramoto model on dynamic random graphs ⋮ Local weak convergence for sparse networks of interacting processes ⋮ Long-term stability of interacting Hawkes processes on random graphs ⋮ Two-community noisy Kuramoto model ⋮ Central limit theorems for global and local empirical measures of diffusions on Erdős-Rényi graphs ⋮ Graphon mean field systems ⋮ Weakly interacting oscillators on dense random graphs ⋮ Long time dynamics for interacting oscillators on graphs
Cites Work
- Unnamed Item
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- Clarification and complement to ``Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons
- Waves in neural media. From single neurons to neural fields
- Convergent sequences of dense graphs. II. Multiway cuts and statistical physics
- Synchronization and random long time dynamics for mean-field plane rotators
- Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction
- A note on dynamical models on random graphs and Fokker-Planck equations
- Tightness of probabilities on C([0,1;\(S_ p\)) and D([0,1];\(S_ p\))]
- Limits of randomly grown graph sequences
- Mean field limit for disordered diffusions with singular interactions
- Limits of dense graph sequences
- Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing
- Dynamics of pattern formation in lateral-inhibition type neural fields
- The mean field analysis of the Kuramoto model on graphs. I: The mean field equation and transition point formulas
- An \(L^{p}\) theory of sparse graph convergence. II: LD convergence, quotients and right convergence
- Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels
- Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
- Weakly interacting particle systems on inhomogeneous random graphs
- Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions
- Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction: a slow-fast dynamics approach
- Stochastic neural field equations: a rigorous footing
- Long time dynamics and disorder-induced traveling waves in the stochastic Kuramoto model
- Path large deviations for interacting diffusions with local mean-field interactions in random environment
- The nonlinear heat equation on \(W\)-random graphs
- A General Framework for Stochastic Traveling Waves and Patterns, with Application to Neural Field Equations
- A Multiscale Analysis of Traveling Waves in Stochastic Neural Fields
- The Nonlinear Heat Equation on Dense Graphs and Graph Limits
- Front Propagation in Stochastic Neural Fields: A Rigorous Mathematical Framework
- Spatiotemporal dynamics of continuum neural fields
- Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
- Concentration Inequalities and Martingale Inequalities: A Survey
- Some remarks about backward itô formula and applications
- Mean field dynamics of a Wilson–Cowan neuronal network with nonlinear coupling term
- Rigorous Derivation of the Nonlocal Reaction-Diffusion Fitzhugh--Nagumo System
- The Mean Field Equation for the Kuramoto Model on Graph Sequences with Non-Lipschitz Limit
- Threshold of Front Propagation in Neural Fields: An Interface Dynamics Approach
- Real Analysis and Probability
- Transitions in Active Rotator Systems: Invariant Hyperbolic Manifold Approach
- An 𝐿^{𝑝} theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions
- Continuation of Localized Coherent Structures in Nonlocal Neural Field Equations
- CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS
- The Semilinear Heat Equation on Sparse Random Graphs
- Optimal Transport
