I tiakina i:
Ngā taipitopito rārangi puna kōrero
Kaituhi matua: li, yuanjian
Hōputu: Recurso digital
Reo:
I whakaputaina: Zenodo 2026
Urunga tuihono:https://doi.org/10.5281/zenodo.19325495
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Rārangi ihirangi:
  • <p>We develop the mathematical foundations of the information Ricci flow on the infinite-dimensional information manifold of smooth positive probability densities on a compact Riemannian manifold. We construct the Fisher--Rao metric, derive the geodesic equation, establish local well-posedness, and introduce an information Ricci flow coupling the base metric and the density. We define an information entropy functional of Perelman type, prove its monotonicity, and introduce the notions of information singularities and information horizons. Several original theorems and equations are proved, establishing the analytic and geometric structure of the information Ricci flow.</p>