Skip to content
DraconiticResearch
Search Sources API
182,469 studies31 sourcesUpdated 24 min ago
PreprintCC BY 4.0arXiv

Autonomous self-harmonic drift in Langevin dynamics causes a compaction of underlying domain for the density of Stochastic Localization

  • Ken Sekimoto
Open at sourcePDFDOICite

Abstract

Our recent research on Langevin dynamics with self-harmonic drift and classical spins has revealed a strong connection to ``Stochastic Localization," a concept attracting attention in the fields of mathematical geometry and data science. Roughly speaking, the former can be viewed as a version of the latter in which the n-dimensional Euclidean space - the domain of the probability distribution function appearing in the latter - is ``compactified'' to the surface of an n-dimensional sphere. By comparing the two frameworks, we argue that this compactification is a consequence of requiring the drift to be autonomous. The relationship between the two approaches may expand the scope of Stochastic Localization.

Related

  1. Local Approximation of A-Harmonic Functions and the Super-Localization Conjecture
    Moritz Hauck, Chupeng Ma, Daniel Peterseim
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  2. Stochastic maximal Lp-regularity for non-autonomous evolution equations with fractional derivative in UMD spaces
    Lu Lu Tao, Jia Wei He
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv
  3. Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow
    Robert Lasarzik, Stefan Metzger, Maximilian E. V. Reiter
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Extensions of a family of Linear Cycle Sets whose underlying group is a product of two cyclic groups
    Jorge Guccione, Juan José Guccione, Christian Valqui
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Freeness of Arrangements with Regular Underlying Matroids
    Weikang Liang, Suijie Wang
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{sekimoto2026autonomous,
  title = {{Autonomous self-harmonic drift in Langevin dynamics causes a compaction of underlying domain for the density of Stochastic Localization}},
  author = {Ken Sekimoto},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.36232},
  eprint = {2609.36232},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36232},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Autonomous self-harmonic drift in Langevin dynamics causes a compaction of underlying domain for the density of Stochastic Localization
AU  - Ken Sekimoto
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.36232
UR  - https://arxiv.org/abs/2609.36232
AB  - Our recent research on Langevin dynamics with self-harmonic drift and classical spins has revealed a strong connection to ``Stochastic Localization," a concept attracting attention in the fields of mathematical geometry and data science. Roughly speaking, the former can be viewed as a version of the latter in which the n-dimensional Euclidean space - the domain of the probability distribution function appearing in the latter - is ``compactified'' to the surface of an n-dimensional sphere. By comparing the two frameworks, we argue that this compactification is a consequence of requiring the drift to be autonomous. The relationship between the two approaches may expand the scope of Stochastic Localization.
ER  -