arXiv research

The paper solves equations for Higgs bundles on non-Kähler manifolds.

The article proves a complex analytic inequality for stable Q-sheaves on Kähler varieties.

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively …

Real analytic maps can be unstable even if infinitesimal changes are stable.

We provide a new topological obstruction for complete stable minimal hypersurfaces in R^n. For $n\geq 4$, we prove that any complete orientable stable hypersurfaces in R^n has only one end. This follows from a more general analytic theorem we prove in the paper.

The paper proves uniform stable radius and Milnor number equality for specific mappings.

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…

Geometric Invariant Theory applied to Kähler manifolds yields analytic models for vector bundles.

The paper proves stability of certain singularities in integrable systems.

Analytical tools for pricing power options in Lévy models.

New proof for stable reduction theorem using Kähler-Einstein metrics.

A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.

Generators for the module of vector fields liftable over corank 1 stable complex analytic maps from an n-manifold to an (n+1)-manifold are found. This is applied to the classification of the singularities occuring in generic one-parameter families of maps between these spaces.

An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to an exact sequence. The residue kernel defines the vanishing residue subsheaf. F…

New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.

We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $α$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the Lévy propagator. Using distributional and $\mathbb{C}^n$ tools, we derive an analytic …

Investigates stock models using tempered stable processes for option pricing.

We show that for complex analytic K3 surfaces any torsion class in H^2(X,O_X^*) comes from an Azumaya algebra. In other words, the Brauer group equals the cohomological Brauer group. For algebraic surfaces, such results go back to Grothendieck. In our situation, we use twistor spaces to deform a given analytic K3 surfa…

By the work of Hong and Tian it is known that given a holomorphic vector bundle E over a compact Kahler manifold X, the Yang-Mills flow converges away from an analytic singular set. If E is semi-stable, then the limiting metric is Hermitian-Einstein and will decompose the limiting bundle into a direct sum of stable bun…

Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…

In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric depends analytically on the weights and the stable Higgs bundle. This gives a Higgs bundle generalisation of a theorem of McOwen on the existe…

We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of stable curves with marked points. We provide an explicit characterization of pointed stable differentials in the boundary of the closure, bot…

This paper uses Gaussian Process and converse Lyapunov function to estimate power system ROA.

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices …

In this paper, certain natural and elementary polygonal objects in Euclidean space, {\it the stable polygons}, are introduced, and the novel moduli spaces ${\bfmit M}_{{\bf r}, ε}$ of stable polygons are constructed as complex analytic spaces. Quite unexpectedly, these new moduli spaces are shown to be projective and i…

Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its propert…

Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…

Proves analyticity of quasinormal modes in Kerr and Kerr-de Sitter spacetimes.

In this paper, a systematic method is given to construct all liftable vector fields over an analytic multigerm $f: (\mathbb{K}^n, S)\to (\mathbb{K}^p,0)$ of corank at most one admitting a one-parameter stable unfolding.

We prove the Arnold conjecture for closed symplectic manifolds with $π_2(M)=0$ and $\cat M=\dim M$. Furthermore, we prove an analog of the Lusternik-Schnirelmann theorem for functions with ``generalized hyperbolicity'' property.

Proves solvability of general inverse σ_k equations with constant coefficients.

We prove the existence of a Hermitian-Einstein metric on holomorphic vector bundles with a Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying Kähler manifolds. We also study the curvature decay of the Hermitian-Einstein metrics. It is useful for the study of the class…

This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial differential equation (FPDE) system. Using the technique of approximation we prove t…

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilised to undertake capital estimation. It has however become well accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss…

Study on liquid-vapor interfaces in stable equilibrium without assuming prior regularity.

A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redun…

Constructs a space for stable holomorphic submersions over a fixed base.

Proposes a method to learn stable invariant sets in dynamical systems.

Let $N$ be a Riemannian manifold and consider a stationary union of three or more $C^{1,μ}$ hypersurfaces-with-boundary $M_k$ in $N$ with a common boundary $Γ$. We show that if $N$ is smooth, then $Γ$ is smooth and each $M_k$ is smooth up to $Γ$ (real analytic in the case $N$ is real analytic). Consequently we strength…

We provide a sufficient condition for polarisations of Fano varieties to be K-stable in terms of Tian's alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system associated to the polarisation. This generalises a result of Odaka-Sano in the anti-canonically polari…

Constructs stable Hilbert bundles on curves using Diophantine approximation.

Study of height jumps in Ceresa cycle using asymptotic Hodge theory.

We show that at generic points blow-ups/tangents of differentiability spaces are still differentiability spaces; this implies that an analytic condition introduced by Keith as an inequality (and later proved to actually be an equality) passes to tangents. As an application, we characterize the $p$-weak gradient on iter…

Unified approach classifies stable and minimal elastic curves.

Approximate 3D elastic curves with exact constraints

We establish an explicit pricing formula for the class of Lévy-stable models with maximal negative asymmetry (Log-Lévy model with finite moments and stability parameter $1<α\leq 2$) in the form of rapidly converging series. The series is obtained with help of Mellin transform and the residue theory in $\mathbb{C}^2$. T…

Local gluing connects flow lines in finite time intervals.

New MCMC method tackles heavy tailed distributions using Fourier transforms.