{
  "annotation_id": "47c27874-0079-46b9-965f-2554b1b9be72",
  "date_created": "2026-03-02T18:01:10.860000Z",
  "date_modified": "2026-03-02T18:01:10.860000Z",
  "file_hash": "a7bb9d85a705e66c2f294a83e3eaef71f41e22fcb71a1fa1026fe031e95de255",
  "private": false,
  "record": {
    "abstract": "In this paper we explore the functional correlation approach to operational\nrisk. We consider networks with heterogeneous a-priori conditional and\nunconditional failure probability. In the limit of sparse connectivity,\nself-consistent expressions for the dynamical evolution of order parameters are\nobtained. Under equilibrium conditions, expressions for the stationary states\nare also obtained. The consequences of the analytical theory developed are\nanalyzed using phase diagrams. We find co-existence of operational and\nnon-operational phases, much as in liquid-gas systems. Such systems are\nsusceptible to discontinuous phase transitions from the operational to\nnon-operational phase via catastrophic breakdown. We find this feature to be\nrobust against variation of the microscopic modelling assumptions.",
    "arxiv_id": "physics/0609130",
    "authors": [
      "Kartik Anand",
      "Reimer K\u00fchn"
    ],
    "categories": [
      "physics.soc-ph",
      "cond-mat.dis-nn",
      "q-fin.RM"
    ],
    "doi": "10.1103/PhysRevE.75.016111",
    "title": "Phase Transitions in Operational Risk",
    "url": "https://arxiv.org/abs/physics/0609130"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "066c9a97-28a1-49d9-bbca-5a4a2270f03e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}