Cutoff for a class of auto‐regressive models with vanishing additive noise
研究了一类自回归马尔可夫链的收敛速度，当噪声消失时出现截断现象，该模型与德·菲内蒂提出的部分可交换数据贝叶斯方案有关。
Abstract We analyze the convergence rates for a family of auto‐regressive Markov chains on Euclidean space depending on a parameter , 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.