{"paper":{"title":"On the Gap and Time Interval between the First Two Maxima of Long Continuous Time Random Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Gregory Schehr, Philippe Mounaix, Satya N. Majumdar","submitted_at":"2015-09-02T07:12:43Z","abstract_excerpt":"We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval $T$ where at each time step the walker waits a random time $\\tau$, before performing a jump drawn from a symmetric continuous probability distribution function (PDF) $f(\\eta)$, of L\\'evy index $0 < \\mu \\leq 2$. Our study includes the case where the waiting time PDF $\\Psi(\\tau)$ has a power law tail, $\\Psi(\\tau) \\propto \\tau^{-1 - \\gamma}$, with $0< \\gamma < 1$, such that the average time between two consecutive jumps is infinite. The random motion is sub-diffusive if $\\gamma < \\mu/2$ (and super-diffusive "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00582","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"}