{"paper":{"title":"Random Walks, Electric Networks and The Transience Class problem of Sandpiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","cs.SI","math-ph","math.MP"],"primary_cat":"cs.DM","authors_text":"Ayush Choure, Sundar Vishwanathan","submitted_at":"2011-05-17T13:25:19Z","abstract_excerpt":"The Abelian Sandpile Model is a discrete diffusion process defined on graphs (Dhar \\cite{DD90}, Dhar et al. \\cite{DD95}) which serves as the standard model of \\textit{self-organized criticality}. The transience class of a sandpile is defined as the maximum number of particles that can be added without making the system recurrent (\\cite{BT05}). We develop the theory of discrete diffusions in contrast to continuous harmonic functions on graphs and establish deep connections between standard results in the study of random walks on graphs and sandpiles on graphs. Using this connection and building"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3368","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"}