We develop an extension of the classical model of DeGroot (1974) to a continuum of agents when they interact among them according to a DiKernel. We show that, under some regularity assumptions, the continuous model is the limit case of the discrete one. Additionally, we establish sufficient conditions for the emergence of consensus. We provide some applications of these results. First, we establish a canonical way to reduce the dimensionality of matrices by comparing matrices of different dimensions in the space of DiKernels. Then, we develop a model of Lobby Competition where two lobbies compete to bias the opinion of a continuum of agents. We give sufficient conditions for the existence of a Nash Equilibrium and study their relation with the equilibria of discretizations of the game. Finally, we characterize the equilibrium for a particular case of DiKernels.
Quantitative mode stability for the wave equation on the Kerr-Newman spacetime
Risk-Aware Objective-Based Forecasting in Inertia Management
Chainalysis: Geography of Cryptocurrency 2023
Periodicity in Cryptocurrency Volatility and Liquidity
Impact of Geometric Uncertainty on the Computation of Abdominal Aortic Aneurysm Wall Strain
Simulation-based Bayesian inference with ameliorative learned summary statistics -- Part I