Related papers: Heat Kernel Expansions for Distributional Backgrou…
Suppose that $d\ge 1$ and $\alpha\in (0, 2)$. In this paper, by using probabilistic methods, we establish sharp two-sided pointwise estimates for the Dirichlet heat kernels of $\{\Delta+ a^\alpha \Delta^{\alpha/2}; \ a\in (0, 1]\}$ on…
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a…
In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
We propose an efficient regularization method for functional determinants of radial operators using heat kernel coefficients. Our key finding is a systematic way to identify heat kernel coefficients in the angular momentum space. We…
In the case of the heat equation $u_t=u_{xx}+Vu$ on the real line there are some remarkable potentials $V$ for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula. We show that a…
We obtain pointwise lower bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in $\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close…
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…
The temperature gradient of microwave background radiation (CMBR) is calculated in the Self Consistent Model. An expected values for Hubble parameter have been presented in two different cases. In the first case the temperature is treated…
We point out that using the heat kernel on a cone to compute the first quantum correction to the entropy of Rindler space does not yield the correct temperature dependence. In order to obtain the physics at arbitrary temperature one must…
A computer aided high temperature expansion of the magnetic susceptibility and the magnetic specific heat is presented and demonstrated for frustrated and unfrustrated spin chains. The results are analytic in nature since the calculations…
The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that the relevant partial differential operator appears in the…
The Heat Kernel Method is applied to the constituent quark model. We calculate the effect of thermal quark fluctuations on the meson action and the resulting quark condensate and pi pi-scattering amplitude at finite temperature. The quarks…
Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and…
The quark fluctuation propagator is evaluated. It defines the diffusion coefficient in the vicinity of the phase transition and the gradient term in the Ginzburg-Landau functional.
We study the quantum propagation of particles in cosmological backgrounds, by considering a doublet of massive scalar fields propagating in an expanding universe, possibly filled with radiation. We focus on the dissipative effects related…
We consider the stochastic differential equation on $\mathbb{R}^d$ given by $$ \, \mathrm{d}X_t = b(t,X_t) \, \mathrm{d}t + \, \mathrm{d} B_t, $$ where $B$ is a Brownian motion and $b$ is considered to be a distribution of regularity $ >…
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…
We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…
The fragmentation equation is commonly expressed in terms of two functions, the rate of fragmentation and the mean number of fragments. In the case of binary fragmentation an alternative description is possible based on the fragmentation…