{
  "annotation_id": "9262687d-d9a1-4261-accf-30cf3559f74f",
  "date_created": "2026-02-17T05:53:24.325000Z",
  "date_modified": "2026-02-17T05:53:24.325000Z",
  "file_hash": "9a4ea9f9c724e9ecf38faca067c82699d908446038b8a52ebf8bd174f7b05e0d",
  "private": false,
  "record": {
    "abstract": "We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in projection-based algorithms, learning in games, and systems with discontinuous decision rules, where classical Feller assumptions and small-noise or large-deviation techniques are not applicable.\n  Under a global Lyapunov condition, we prove that any weak limit of invariant measures must be supported on the set of fixed points of the associated deterministic dynamics. Beyond localization, we establish a sharp exclusion principle for unstable equilibria: strict local maxima and saddle points of the Lyapunov function are shown to carry zero mass in limiting invariant measures under explicit and verifiable non-degeneracy conditions.\n  Our analysis identifies a local mechanism driven by Lyapunov geometry and persistent variance, showing that equilibrium selection in constant-step dynamics is governed by typical fluctuations rather than rare events. These results provide a probabilistic foundation for stability and equilibrium selection in stochastic systems with persistent noise and weak regularity.",
    "arxiv_id": "2601.09880",
    "authors": [
      "Jean-Gabriel Attali"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Asymptotic Stability and Equilibrium Selection in Quasi-Feller Systems with Minimal Moment Conditions",
    "url": "https://arxiv.org/abs/2601.09880",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5bd0ebc6-85c8-45d0-913b-e0a7a69d26aa",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}