{
  "abstract": "We compute exactly the covariance between the maximum $M$ and the number of records $K$ in a discrete time series of $n$ entries as a quantitative probe of the history leading to an extreme event. For continuous IID series, with a common probability distribution function (PDF) $p(x)$, we find the striking result that $M$ and $K$ are uncorrelated for any $n \\geq 1$. We show that this independence is rather fragile and the covariance $C_q(n)$ between $M$ and $K$ becomes nonzero when $p(x)$ becomes discontinuous due to a delta-component at $x=0$ with an amplitude $0< q < 1$. This time series models the occurrence of dry days with probability $q$ in a precipitation time series when there is no rainfall. We show that there is an interesting shape transition at a critical value $q_c$ where the covariance $C_q(n)$, as a function of $n$, changes from monotonic ($q<q_c$) to non monotonic behavior (for $q>q_c$). We compute the critical strength $q_c$ exactly. Furthermore, for large $n$, we show that $C_q(n)$ decays as a power law, with an exponent that depends on the tail of $p(x)$. We then compare our theoretical predictions with real precipitation data from several weather stations across Germany, finding a very good agreement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23217",
  "author_total": 3,
  "authors": [
    {
      "name": "Satya N. Majumdar"
    },
    {
      "name": "Sanjib Sabhapandit"
    },
    {
      "name": "Gregory Schehr"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91e4a5j7k7rz9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23217",
  "fulltext_url": null,
  "id": "91e4a5j7k7rz9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23217",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "2002|Complex Systems and Time Series Analysis"
    ]
  ],
  "openalex": "W7222945344",
  "pdf_url": "https://arxiv.org/pdf/2610.23217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91e4a5j7k7rz9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.23217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23217"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Emergence of Correlations Between Records and Maximum in Random Time Series",
  "title_text": "Emergence of Correlations Between Records and Maximum in Random Time Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/91e4a5j7k7rz9",
  "venue": "arXiv",
  "versions": []
}