{"paper":{"title":"The Dual Potential, the involution kernel and Transport in Ergodic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.OC","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Elismar R. Oliveira, Philippe Thieullen","submitted_at":"2011-11-01T19:40:29Z","abstract_excerpt":"Consider the shift $\\sigma$ acting on the Bernoulli space $\\Sigma={1,2,...,n}^\\mathbb{N}$. We denote $\\hat{\\Sigma}= {1,2,...,n}^\\mathbb{Z}$. We analyze several properties of the maximizing probability $\\mu_{\\infty,A}$ of a Holder potential $A: \\Sigma \\to \\mathbb{R}$. Associated to $A(x)$, via the involution kernel, $W: \\hat{\\Sigma} \\to \\mathbb{R}$, it is known that can we get the dual potential $A^*(y)$, where $(x,y)\\in \\hat{\\Sigma}$. Consider $\\mu_{\\infty, A^*}$ a maximizing probability for $A^*$. We would like to consider the transport problem from $\\mu_{\\infty,A}$ to $\\mu_{\\infty,A^*}$. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0281","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"}