{"paper":{"title":"Weak dependence for a class of local functionals of Markov chains on $\\mathbb{Z}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Antonella Marchesiello, Carlo Boldrighini, Chiara Saffirio","submitted_at":"2015-01-29T15:42:52Z","abstract_excerpt":"In some papers on infinite Markov chains in $\\mathbb{Z}^d$, and notably in the work of R.A. Minlos and collaborators, one can prove the existence of a spectral gap for a suitable subspace of local functions. We consider functions of the type $f(\\widehat \\eta)$, where $\\widehat \\eta= \\{\\eta_{t}\\}_{t=0}^{\\infty}$ is the sequence of the states, and $f$ is local. In the case of a simple example of random walk in random environment with mutual interaction we show that there is a natural class of functions $f$, related to the H\\\"older continuos functions $\\mathcal C^{\\alpha}$on the torus $T^{1}$, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07486","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}