The biLipschitz Geometry of Complex Curves: An Algebraic Approach

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Complex Manifolds ◽

10.1515/coma-2017-0005 ◽

2017 ◽

Vol 4 (1) ◽

pp. 43-72 ◽

Cited By ~ 1

Author(s):

Martin de Borbon

Keyword(s):

Vector Field ◽

Einstein Metrics ◽

Projective Line ◽

Tangent Cones ◽

Reeb Vector ◽

Reeb Vector Field ◽

Complex Curves ◽

Complex Dimensions ◽

Irregular Case ◽

Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

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Target space entanglement in quantum mechanics of fermions and matrices

Journal of High Energy Physics ◽

10.1007/jhep08(2021)046 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Sotaro Sugishita

Keyword(s):

Mutual Information ◽

Ground State ◽

Entanglement Entropy ◽

Algebraic Approach ◽

Upper Bounds ◽

Wave Functions ◽

Target Space ◽

Single Interval ◽

Area Law ◽

Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

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