{
  "annotation_id": "fde53177-1cdf-4e13-896f-3a20d5cb3966",
  "date_created": "2026-02-17T05:53:11.758000Z",
  "date_modified": "2026-02-17T05:53:11.758000Z",
  "file_hash": "3789062271b4eac9cfa3d5c6e03713bcfefb10cffdd61a80051e65cbaa454008",
  "private": false,
  "record": {
    "abstract": "We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov\u0027s theorem) or specific mixing conditions, our result requires only two conditions: (1) control over the variance of the empirical moments, and (2) a flexible tail condition we term $\\Psi_{r_n}$-sub-Gaussianity. This approach allows for significant dependencies between variables, provided their algebraic moments behave predictably. The proof uses the method of moments combined with a polynomial approximation of Lipschitz functions via Jackson kernels, allowing us to translate moment concentration into topological concentration.",
    "arxiv_id": "2601.07228",
    "authors": [
      "Arash A. Amini",
      "Luciano Vinas"
    ],
    "categories": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Wasserstein Concentration of Empirical Measures for Dependent Data via the Method of Moments",
    "url": "https://arxiv.org/abs/2601.07228",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "814d2524-4521-4e81-a623-08621edc6061",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}