{
  "annotation_id": "f5d554d5-b228-4e6d-8e33-623028090710",
  "date_created": "2026-03-02T18:01:07.938000Z",
  "date_modified": "2026-03-02T18:01:07.938000Z",
  "file_hash": "d7f8a0f3b300f89eb39c8a92a5dc6a376899b96fbbf58ed81f35570e1e7037cc",
  "private": false,
  "record": {
    "abstract": "In this paper, we quantitatively investigate the statistical properties of a\nstatistical ensemble of stock prices. We selected 1200 stocks traded on the\nTokyo Stock Exchange, and formed a statistical ensemble of daily stock prices\nfor each trading day in the 3-year period from January 4, 1999 to December 28,\n2001, corresponding to the period of the forming of the internet bubble in\nJapn, and its bursting in the Japanese stock market. We found that the tail of\nthe complementary cumulative distribution function of the ensemble of stock\nprices in the high value of the price is well described by a power-law\ndistribution, $ P(S\u003ex) \\sim x^{-\\alpha} $, with an exponent that moves in the\nrange of $ 1.09 \u003c \\alpha \u003c 1.27 $. Furthermore, we found that as the power-law\nexponents $ \\alpha $ approached unity, the bubbles collapsed. This suggests\nthat Zipf\u0027s law for stock prices is a sign that bubbles are going to burst.\n  PACS: 89.65.Gh",
    "arxiv_id": "physics/0603138",
    "authors": [
      "Taisei Kaizoji"
    ],
    "categories": [
      "physics.soc-ph",
      "physics.data-an",
      "q-fin.ST"
    ],
    "doi": "10.1143/PTPS.162.165",
    "journal_ref": "Progress of Theoretical Physics Supplement 162 (2006) 165-172",
    "title": "Power laws and market crashes",
    "url": "https://arxiv.org/abs/physics/0603138"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "487ebe16-e6b0-4257-97d9-38b2561101b9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}