arXiv research

We prove the weak stability of expanding gradient Ricci solitons with positive curvature operator and quadratic curvature decay at infinity.

Stability results for complex Monge-Ampère equations in various classes.

Stability of Yang-Mills connections' Morse indices and nullity in 4D.

Proposes indifference pricing to estimate weak information value.

Paper studies identifiability and stability of drifting fields in generative modeling.

It is known that the totally umbilical hypersurfaces in the (n+1)-dimensional spheres are characterized as the only hypersurfaces with weak stability index 0. That is, a compact hypersurface with constant mean curvature, cmc, in S^{n+1}, different from an Euclidean sphere, must have stability index greater than or equa…

The paper explores identifiability and stability in drifting fields using companion-elliptic kernels.

The study establishes stability in WMOT, crucial for finance with imprecise data.

Characterizes toroidal and semi-toric compactifications as log minimal models and applies to weak K-moduli.

Study proves existence, uniqueness, and stability for specific stochastic Volterra equations.

We show that every finite volume hyperbolic manifold of dimension greater or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation. It will turn ou…

Study proves stability and uniqueness for a specific type of flow.

Proves stability in Weyl polytopes using optimal transport.

Boosting framework for vector-valued prediction with geometric stability.

In this paper, we prove that on a Fano manifold $M$ which admits a Kähler-Ricci soliton $(\om,X)$, if the initial Kähler metric $\om_{\vphi_0}$ is close to $\om$ in some weak sense, then the weak Kähler-Ricci flow exists globally and converges in Cheeger-Gromov sense. Moreover, if $\vphi_0$ is also $K_X$-invariant, the…

The paper proves stability of critical points for conformally invariant Lagrangians.

We prove the existence of weak solutions of complex $m-$Hessian equations on compact Hermitian manifolds for the nonnegative right hand side belonging to $L^p, p>n/m$ ($n$ is the dimension of the manifold). For smooth, positive data the equation has been recently solved by Szekelyhidi and Zhang. We also give a stabilit…

Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $π_1, π_2, \ldots$ converges weakly to a transport plan $π$, then $π$ is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for th…

We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz func…

New approach finds solutions to games with unbounded controls.

Study on stability of optimal transport problems for probability measures.

We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over $\mathbb{C}$ attached to character polynomials. Our approach interprets the stabilization as a probabilistic phenomenon based on the asymptotic independence of certain *motivic random variables*, an…

Extends martingale transport for robust finance problems.

We prove geometric and cohomological stabilization results for the universal smooth degree $d$ hypersurface section of a fixed smooth projective variety as $d$ goes to infinity. We show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed Grothendieck ring of variet…

Study Kähler metrics on complex tori with almost non-negative scalar curvature.

Proves stability condition for Lagrangian sections in toric weak Fano manifolds.

Weak supervision challenges black-box models, suggesting fusion of modeling cultures.

Establishes relationships between prudence and stability properties of risk functionals.

We study algebro-geometric consequences of the quantised extremal Kähler metrics, introduced in the previous work of the author. We prove that the existence of quantised extremal metrics implies weak relative Chow polystability. As a consequence, we obtain asymptotic weak relative Chow polystability and $K$-semistabili…

Paper analyzes stability and forgetting in score-based generative models.

Randomness is crucial for stability in learning and statistics, especially for differential privacy.

In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable finite-sample control of the number of false positives. Its benefits were demonstrated …

We study the deformed Hermitian-Yang-Mills (dHYM) equation, which is mirror to the special Lagrangian equation, from the variational point of view via an infinite dimensional GIT problem mirror to Thomas' GIT picture for special Lagrangians. This gives rise to infinite dimensional manifold $\mathcal{H}$ mirror to Solom…

Study proves stability of big bang singularity in complex system.

We provide a dual characterisation of the weak$^*$-closure of a finite sum of cones in $L^\infty$ adapted to a discrete time filtration $\mathcal{F}_t$: the $t^{th}$ cone in the sum contains bounded random variables that are $\mathcal{F}_t$-measurable. Hence we obtain a generalisation of Delbaen's m-stability condition…

Study special Lagrangian sections in Calabi-Yau threefolds, showing stability conditions imply isomorphism to special Lagrangians.

Authors create stable proper biharmonic maps from unit ball to spheres.

Paper studies central bank's strategy to control systemic risk in interbank system.

Third in a series, this paper constructs non-trivial Cayley fibrations with conical singularities.

In this follow up work to [45, 33, 32, 46] we introduce and study a notion of geodesic stability restricted to rays with prescribed singularity types. A number of notions of interest fit into this framework, in particular algebraic- and transcendental K-polystability, equivariant K-polystability, and the geodesic K-pol…

This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the model for a second-grade non-Newtonian fluid. We study the analytical and geometrical properties of the Lagrangian flow map. We prove existen…

Two new algorithms solve privacy-constrained SVI and SSP problems.

The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.

The equivalence (or weak equivalence) classes of orientation-preserving free actions of a finite group G on an orientable 3-dimensional handlebody of genus g can be enumerated in terms of sets of generators of G. They correspond to the equivalence classes of generating n-vectors of elements of G, where n=1+(g-1)/|G|, u…

AANets balance stability and plasticity in CIL.

Motivation: Biomarker discovery from high-dimensional data is a crucial problem with enormous applications in biology and medicine. It is also extremely challenging from a statistical viewpoint, but surprisingly few studies have investigated the relative strengths and weaknesses of the plethora of existing feature sele…

Studied how SGD's stability regularization affects generalization in neural networks.

The paper proves existence and instability of weak $r$-harmonic maps.