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In this work we study a 3-state ($+1$, $-1$, $0$) opinion model in the presence of noise and disorder. We consider pairwise competitive interactions, with a fraction $p$ of those interactions being negative (disorder). Moreover, there is a…
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The voter model on $\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of…
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The electoral college of voting system for the US presidential election is analogous to a coarse graining procedure commonly used to study phase transitions in physical systems. In a recent paper, opinion dynamics models manifesting a phase…
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The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group…
A model for opinion dynamics (Model I) has been recently introduced in which the binary opinions of the individuals are determined according to the size of their neighboring domains (population having the same opinion). The coarsening…
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Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…