{"paper":{"title":"Scalar conservation laws with monotone pure-jump Markov initial conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David C. Kaspar, Fraydoun Rezakhanlou","submitted_at":"2015-02-17T04:50:25Z","abstract_excerpt":"In 2010 Menon and Srinivasan published a conjecture for the statistical structure of solutions $\\rho$ to scalar conservation laws with certain Markov initial conditions, proposing a kinetic equation that should suffice to describe $\\rho(x,t)$ as a stochastic process in $x$ with $t$ fixed. In this article we verify an analogue of the conjecture for initial conditions which are bounded, monotone, and piecewise constant. Our argument uses a particle system representation of $\\rho(x,t)$ over $0 \\leq x \\leq L$ for $L > 0$, with a suitable random boundary condition at $x = L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04795","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"}