2007/11/23 by Christof Kuelske, C. Kuelske, Kuelske, C. +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60K35 #82B20 #82B26 #Complex Systems and Time Series Analysis #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K35 #msc:82B20 #msc:82B26
paper · pdf · doi:10.48550/arxiv.0711.3764
32 pages
arxiv created 2007/11/23 · openalex publication_date 2007/11/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general method to derive continuity estimates for conditional probabilities of general (possibly continuous) spin models sub jected to local transformations. Such systems arise in the study of a stochastic time-evolution of Gibbs measures or as noisy observations. We exhibit the minimal necessary structure for such double-layer systems. Assuming no a priori metric on the local state spaces, we define the posterior metric on the local image space. We show that it allows in a natural way to divide the local part of the continuity estimates from the spatial part (which is treated by Dobrushin uniqueness here). We show in the concrete example of the time evolution of rotators on the q-1 dimensional sphere how this method can be used to obtain estimates in terms of the familiar Euclidean metric.