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Cutoff for a class of auto‐regressive models with vanishing additive noise

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  • Balázs Gerencsér
  • Andrea Ottolini

Abstract

We analyze the convergence rates for a family of auto‐regressive Markov chains on Euclidean space depending on a parameter n$$ n $$, where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others. The interest in the model comes from the connection with a certain Bayesian scheme introduced by de Finetti in the analysis of partially exchangeable data. Our main result shows that, when n gets large (corresponding to a vanishing noise), a cutoff phenomenon occurs.

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  • Balázs Gerencsér & Andrea Ottolini, 2025. "Cutoff for a class of auto‐regressive models with vanishing additive noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 52(1), pages 314-331, March.
    • Handle: RePEc:bla:scjsta:v:52:y:2025:i:1:p:314-331
    DOI: 10.1111/sjos.12748
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