{"paper":{"title":"Intermittency in a catalytic random medium","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"F. den Hollander, J. G\\\"artner","submitted_at":"2004-06-14T11:17:49Z","abstract_excerpt":"In this paper, we study intermittency for the parabolic Anderson equation $\\partial u/\\partial t=\\kappa\\Delta u+\\xi u$, where $u:\\mathbb{Z}^d\\times [0,\\infty)\\to\\mathbb{R}$, $\\kappa$ is the diffusion constant, $\\Delta$ is the discrete Laplacian and $\\xi:\\mathbb{Z}^d\\times[0,\\infty)\\to\\mathbb {R}$ is a space-time random medium. We focus on the case where $\\xi$ is $\\gamma$ times the random medium that is obtained by running independent simple random walks with diffusion constant $\\rho$ starting from a Poisson random field with intensity $\\nu$. Throughout the paper, we assume that $\\kappa,\\gamma,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406266","kind":"arxiv","version":2},"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"}