{"paper":{"title":"Changes of graph structure of transition probability matrices indicate the slowest kinetic relaxations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Kensuke S. Ikeda, Teruaki Okushima, Tomoaki Niiyama, Yasushi Shimizu","submitted_at":"2018-09-15T06:01:34Z","abstract_excerpt":"Graphs of the most probable transitions for a transition probability matrix, $e^{\\tau K}$, i.e., the time evolution matrix of the transition rate matrix $K$ over a finite time interval $\\tau$, are considered. We study how the graph structures of the most probable transitions change as functions of $\\tau$, thereby elucidating that a kinetic threshold $\\tau_g$ for the graph structures exists. Namely, for $\\tau<\\tau_g$, the number of connected graph components are constant. In contrast, for $\\tau\\geq \\tau_g$, recombinations of most probable transitions over the connected graph components occur mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05654","kind":"arxiv","version":1},"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"}