Related papers: Kernel estimates for nonautonomous Kolmogorov equa…

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…

We prove Cameron-Martin type quasi-invariance results for the heat kernel measure of infinite-dimensional Kolmogorov and related diffusions. We first study quantitative functional inequalities for appropriate finite-dimensional…

Let $L$ be a closed, densely defined operator of type $ \omega $ on $ L^2(\mathbb{R}^n)$ with $0 \leq \omega < \pi/2 $. We assume that $ L $ possesses a bounded $ H_\infty $-functional calculus and that its heat kernel satisfies suitable…

Consider the Schr\"odinger operator $ \mathcal L^V=-\Delta+V $ on $\R^d$, where $V:\R^d\to [0,\infty)$ is a nonnegative and locally bounded potential on $\R^d$ so that for all $x\in \R^d$ with $|x|\ge 1$, $c_1g(|x|)\le V(x)\le c_2g(|x|)$…

We consider the heat equation associated with a class of hypoelliptic operators of Kolmogorov-Fokker-Planck type in dimension two. We explicitly compute the first meaningful coefficient of the small time asymptotic expansion of the heat…

We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and…

We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain…

We establish sharp upper and lower bounds on the heat kernel of the fractional Laplace operator perturbed by Hardy-type drift by transferring it to appropriate weighted space with singular weight.

We give the upper and the lower estimates of heat kernels for Schr\"odinger operators $H=-\Delta+V$, with nonnegative and locally bounded potentials $V$ in $\mathbb{R}^d$, $d \geq 1$. We observe a factorization: the contribution of the…

For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and…

The purpose of this article is to establish regularity and pointwise upper bounds for the (relative) fundamental solution of the heat equation associated to the weighted dbar-operator in $L^2(C^n)$ for a certain class of weights. The…

We obtain pointwise upper bounds on the derivatives of the heat kernel on Damek-Ricci spaces. Applying these estimates we prove the $L^p$-boundedness of Littlewood-Paley-Stein operators.

The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic differential second order operator is generalized to manifolds with boundary. The first boundary coefficients of the asymptotic expansion which are…

We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent…

Nash and Sobolev inequalities are known to be equivalent to ultracontractive properties of heat-like Markov semigroups, hence to uniform on-diagonal bounds on their kernel densities. In non ultracontractive settings, such bounds can not…

This paper is an exposition of several questions linking heat kernel measures on infinite dimensional Lie groups, limits associated with critical Sobolev exponents, and Feynmann-Kac measures for sigma models.

By making full use of heat kernel estimates, we establish the integral tests on the zero-one laws of upper and lower bounds for the sample path ranges of symmetric Markov processes. In particular, these results concerning on upper rate…

We derive large time upper bounds for heat kernels on vector bundles of differential forms on a class of non-compact Riemannian manifolds under certain curvature conditions.

We consider fractional Schr\"odinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragm\'en-Lindel\"of theorem for polynomially bounded…