Radicalization Kinetics under Algorithmic Exposure in a Stochastic Multiplex Model of Opinion Dynamics

Abstract

We study how physical mobility, algorithmic exposure, and repulsive social influence interact in a stochastic multiplex model of opinion dynamics. Agents diffuse in physical space while a directed digital network rewires under a conserved attention budget, so digital exposure displaces rather than supplements local interaction. With purely assimilative bounded-confidence influence, opinion-blind long-range exposure reduces locality-induced fragmentation whereas homophilic recommendation preserves echo chambers. When a contested repulsive response to sufficiently distant opinions is activated, this ordering reverses at the reference parameters: a neutral platform reaches the maximal polarization permitted by the bounded opinion space, controversy-seeking curation drives faster initial separation but slows sharply near the boundary, and homophilic curation delays radicalization by suppressing cross-bloc exposure. In a late-stage symmetric two-bloc reduction, any curation kernel maps to a state-dependent cross-bloc exposure profile $p(y)$ and an exact quadrature for the radicalization time. Pointwise-ordered profiles inherit a global kinetic ordering; crossing profiles yield target- and horizon-dependent rankings. For similarity-driven curation the quadrature has a closed form involving the exponential integral. Simulations, finite-size scans to $N=1600$, structural controls, and a well-mixed particle comparison support the mechanism. Heavy-tailed influence strengths are not required for the inversion; in the well-mixed heavy-tail regime they additionally produce a non-self-averaging stable-weighted asymptotic description. Finally, opinion-independent Brownian mobility produces no detectable geographic opinion structure in the explored regime, whereas opinion-dependent drift produces spatial domains through a P\'eclet-controlled crossover near $\chi\ell/D \sim 1$.