Related papers: Heat Kernel Expansions for Distributional Backgrou…
The generator of time-translations on the solution space of the wave equation on stationary spacetimes specialises to the square root of the Laplacian on Riemannian manifolds when the spacetime is ultrastatic. Its spectral analysis…
We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.
Computer algebra methods are applied to investigation of spectral asymptotics of elliptic differential operators on curved manifolds with torsion and in the presence of a gauge field. In this paper we present complete expressions for the…
We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the…
We compute the full asymptotic expansion of the heat kernel Trace$(\exp(-tD^2))$ where $D$ is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The…
The paper deals with point-wise estimates for the heat kernel of a nonlocal convolution type operator with a kernel that decays at least exponentially at infinity. It is shown that the large time behaviour of the heat kernel depends…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
We consider the heat equation associated with a class of second order hypoelliptic H\"{o}rmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a…
In this paper, we firstly establish weighted heat kernel comparison theorems for the weighted heat equation on complete manifolds with radial curvatures bounded, and then by mainly using this conclusion, we can obtain two eigenvalue…
A covariant scattering kernel is a core component in any self-consistent general relativistic radiative transfer formulation in scattering media. An explicit closed-form expression for a covariant Compton scattering kernel with a good…
The contributions to the heat kernel coefficients generated by the corners of the boundary are studied. For this purpose the internal and external sectors of a wedge and a cone are considered. These sectors are obtained by introducing,…
Quenched and annealed heat kernel estimates are established for Fontes-Isopi-Newman (FIN) processes on spaces equipped with a resistance form. These results are new even in the case of the one-dimensional FIN diffusion, and also apply to…
An overview about recent progress in the calculation of the heat kernel and the one-loop effective action in quantum gravity and gauge theories is given. We analyse the general structure of the standard Schwinger-De Witt asymptotic…
In this paper we establish the existence and uniqueness of heat kernels to a large class of time-inhomogenous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates,…
We study reflected jump diffusions on Ahlfors regular domains in general metric measure spaces. Under the condition that the Dirichlet form on the ambient space satisfies a capacity upper bound estimate, we construct an extension operator…
Let us consider a time-dependent differential operator quadratic with respect to the phase variables. Let us consider a multiplication operator defined with the help of a "small" matrix-valued function. Under suitable conditions, we give an…
Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\aa)}$ be the…
These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof…
Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…
Theoretically predicted linear correlation between the volume coefficient of thermal expansion and the thermal heat capacity was investigated for highly symmetrical atomic arrangements. Normalizing the data of these thermodynamic parameters…