Long-Term Behavior and Stability of Interacting Particle Systems with Singular Interactions: A Mathematical Analysis
This paper investigates the long-term dynamics of interacting particle systems with singular interaction kernels, demonstrating that the marginals of the particle distribution remain uniformly bounded in L2 norm over time and particle count, even in configurations far from the mean-field approximation.
Existence and Convergence of Interacting Particle Systems on Graphs with Unbounded Degrees and Jump Rates
This paper establishes the existence and convergence of interacting particle systems on locally finite graphs that can have unbounded degrees and jump rates, relaxing common assumptions in the field.
Interacting Particle Systems on Random Graphs: A Mini-Course Overview
This paper provides an overview of interacting particle systems (IPS) on random graphs, focusing on the Stochastic Ising Model (SIM), Voter Model (VM), and Contact Process (CP), highlighting their behavior on different graph structures and the time scales for critical phenomena.
A Systematic Study of Interactions for Classifying Large-Scale Interacting Particle Systems
This article introduces a novel framework for classifying and constructing interactions in large-scale interacting particle systems, using conserved quantities and graph theory to analyze system behavior for potential application in hydrodynamic limit theory.
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