arXiv research

The paper studies heat kernel asymptotics and proves Morse inequalities.

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

The paper improves asymptotic polybalanced kernels for extremal Kaehler metrics.

Study Szegő kernel on non-compact CR manifolds with specific conditions.

Study on kernel tests for high-dimensional data, focusing on MMD and CLT.

Study asymptotics of Poisson kernel and Green's functions for fractional conformal Laplacian.

Study reproducing kernels on complex Kepler manifolds.

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…

Study on symplectic manifolds, focusing on Bergman kernels and their asymptotic behavior.

Master thesis proves Bergman kernel asymptotics for positive line bundles.

Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.

In this paper, we survey some recent results about the asymptotic expansion of Bergman kernel and we give a Bergman kernel proof of Kodaira embedding theorem.

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper " On the asymptotic expansion of Bergman kernel " (math.DG/040…

New insights into simple kernel smoothing reveal surprising asymptotics.

Study on symplectic manifolds finds asymptotic expansions for Bergman kernels.

We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated to the $k$-th tensor powers of a positive line bundle $L$ in a $\frac{1}{\sqrt{k}}$-neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kähler potential $k\varphi$ …

The paper studies heat kernel asymptotics for Kohn Laplacians on CR manifolds.

We study the asymptotic of the Bergman kernel of the spin$^c$ Dirac operator on high tensor powers of a line bundle.

Optimal kernel improves estimation accuracy in modal statistical methods.

Optimal Biweight kernel and computationally efficient Epanechnikov kernel for modal linear regression.

Study on CR manifolds with $S^1$ action finds Szegő kernel asymptotics.

New tools for analyzing Kähler manifolds, proving operator algebra and asymptotic kernel.

Study shows quantum behavior near infinity in metric asymptotics.

New method for spectral and Bergman kernels under local spectral gap condition.

Study Bergman kernel metrics on degenerating hyperelliptic surfaces.

The paper analyzes heat kernel asymptotics for real powers of Laplacians on manifolds.

The Bergman-Szegő kernel is analyzed for weakly pseudoconvex CR manifolds of finite type.

In this paper we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We then explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small time asymptotics expansion of the heat kernel on the diagonal, expressing them in …

Study on manifolds with kinks and Gaussian kernel behavior.

The study computes Bergman kernels and point process asymptotics on Kähler manifolds.

We analyzed optimism in linear and kernel regression models.

We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^μ\N_μ$. Our objective is to obtain information on the asymptotic expansions of the corresponding r…

Uniform heat kernel and diffusion bridge asymptotics for sub-Riemannian geometry.

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line b…

The paper solves heat kernel asymptotics on non-degenerate CR manifolds.

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate poi…

We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the short-time asymptotic expansion of the heat kernel is calculated explicitly.

We compute the leading and sub-leading terms in the asymptotic expansion of the Szegö kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by relating it to a Bergman kernel over projective space.

Study the heat kernel on quaternionic anti-de Sitter spaces and related spaces.

We show that under very general assumptions the partial Bergman kernel function of sections vanishing along an analytic hypersurface has exponential decay in a neighborhood of the vanishing locus. Considering an ample line bundle, we obtain a uniform estimate of the Bergman kernel function associated to a singular metr…

New test for conditional independence using kernel embeddings.

The paper studies local heat kernel properties on smooth manifolds.

The study examines Bergman kernels on complex manifolds with boundary and their asymptotic expansions.

Study integral kernels on complex symmetric spaces and their Dyson Brownian Motion applications.

Formula for Toeplitz operator kernel on CR manifolds.

We consider a general Hermitian holomorphic line bundle $L$ on a compact complex manifold $M$ and let ${\Box}^q_p$ be the Kodaira Laplacian on $(0,q)$ forms with values in $L^p$. The main result is a complete asymptotic expansion for the semi-classically scaled heat kernel $\exp(-u{\Box}^q_p/p)(x,x)$ along the diagonal…

The study shows inner-product kernels behave similarly to binary kernels in high dimensions.

The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.