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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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4 results for “Polyakov-Alvarez”
Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slitsmath-ph

Formula for Laplacian determinants on polygonal domains with slits.

problem Determining the ζζ-regularized determinant of the Laplacian on polygonal domains with slits.
method Patchwork method for heat trace asymptotics, comparison formula for smooth conformal metrics.
result Polyakov-Alvarez type formula for Laplacian determinants on polygonal domains with slits.
Polyakov-Alvarez formulaζ-determinantFriedrichs extensionDirichlet Laplace-Beltramicurvilinear polygonal domains
2025-01-13abs ↗pdf ↗
Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularitiesmath-ph

The paper proves formulas for determinant determinants of Laplacians on Riemann surfaces with conical singularities.

problem Determinants of Laplacians on Riemann surfaces with conical singularities.
method Polyakov-Alvarez type comparison formulas for determinants of Friedrichs extensions of Laplacians.
result Determine how determinants depend on conical singularities and provide explicit formulas.
Riemann surfacesLaplaciansDeterminantsPolyakov-AlvarezFriedrichs extensions
2019-09-30abs ↗pdf ↗
Brownian loops on non-smooth surfaces and the Polyakov-Alvarez formulamath.PR

For non-smooth surfaces, the measure of Brownian loops is derived using the Polyakov-Alvarez formula.

problem Deriving the measure of Brownian loops on non-smooth surfaces.
method Using the Polyakov-Alvarez formula and heat kernel traces.
result The measure of Brownian loops on non-smooth surfaces is derived and shown to be uniform.
Brownian loopsnon-smooth surfacesPolyakov-Alvarez formulaheat kernel tracesmeasure theory
2023-02-05abs ↗pdf ↗