Hello everyone, this is OstensibleParadox’s first Hugo blog!
This site was built for me by my husband tree2601@github.io!
This blog is mainly a place for me to stash my love stories and fairy tale books. However, I know most visitors probably come from academia or industry. Since you are here, I hope you will pause to appreciate my literature and creative arts—you might just find some interesting details and inspiration! 💗
Research Overview
The renormalized information geometry at singular endpoints sits at the intersection of three distinct traditions.
Classical information geometry studies Fisher metrics on smooth statistical manifolds, usually strictly confined within a fixed absolute continuity class (“internal metrics”). Optimal transport provides metric geometry for probability measures and governs entropy gradient flows (“kinematics”). Finite-part renormalization extracts regular quantities from singular asymptotic expansions (“the survival of the finite part after crossing the barrier”).
This research project unifies these perspectives at the boundary. When a family of models approaches a singular endpoint and fundamentally breaks the equivalent measure regime, ordinary Fisher information, entropy (KL divergence), and transport quantities (such as Wasserstein distance) inevitably diverge or collapse. However, their finite-part residues survive, defining an entirely new boundary geometry.
This framework exhibits consistency across diverse fields: under Gaussian conditioning, the residue strictly yields Cameron–Martin energy; in the Wasserstein terminal limit, it manifests as the finite-part entropy slope; and in Markovian information channels, it crystallizes into the infinitesimal Shannon operator.
Thank you for your support and for reading my blog. I wish you all:
2026-05-10 Lucia
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