Related papers: Heat kernel estimates for Markov processes of dire…

We establish uniform pointwise estimates for the densities of a family of $\alpha$-stable processes with respect to the index $\alpha \in [\alpha_0,2]$ for some $\alpha_0>0$. In addition, we estimate the difference between the heat kernels…

Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…

In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation…

We consider the Dirichlet form given by \sE(f,f)&=&{1/2}\int_{\bR^d}\sum_{i,j=1}^d a_{ij}(x)\frac{\partial f(x)}{\partial x_i} \frac{\partial f(x)}{\partial x_j} dx &+&\int_{\bR^d\times \bR^d} (f(y)-f(x))^2J(x,y)dxdy. Under the assumption…

We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1, 1}$ open sets by using Duhamel formula. We also obtain a…

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…

Let $Z=(Z^{1}, \ldots, Z^{d})$ be the $d$-dimensional L\'evy processes where $Z^{i}$'s are independent $1$-dimensional L\'evy processes with jump kernel $J^{\phi, 1}(u,w) =|u-w|^{-1}\phi(|u-w|)^{-1}$ for $u, w\in \mathbb R$. Here $\phi$ is…

In this article we develop a general method by which one can explicitly evaluate certain sums of $n$-th powers of products of $d\geq 1$ elementary trigonometric functions evaluated at $\mathbf{m}=(m_1,\ldots,m_d)$-th roots of unity. Our…

We establish pointwise estimates for the ground states of some classes of posi- tivity preserving operators. The considered operators are negatively perturbed (by measures) strongly local Dirichlet operators. These estimates will be written…

Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $\mathbb{R}^n$. In particular, in the case when $n=2$ they obtained Gaussian…

We consider heat kernels on Weyl chambers corresponding to Laplacians subject to mixed Dirichlet-Neumann boundary conditions imposed on the boundary. Using purely analytic tools we prove genuinely sharp two-sided global estimates in the…

In this paper, we establish the Hausdorff dimensions of inverse images and collision time sets for a large class of symmetric Markov processes on metric measure spaces. We apply the approach in the works by Hawkes and Jain--Pruitt, and make…

In this paper we study the transition densities for a large class of non-symmetric Markov processes whose jumping kernels decay exponentially or subexponentially. We obtain their upper bounds which also decay at the same rate as their…

We consider the formal SDE dX t = b(t, X t)dt + dZ t , X 0 = x $\in$ R d , (E) where b $\in$ L r ([0, T ], B $\beta$ p,q (R d , R d)) is a time-inhomogeneous Besov drift and Z t is a symmetric d-dimensional $\alpha$-stable process, $\alpha$…

We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates…

We provide sharp two-sided estimates on the Dirichlet heat kernel $k_1(t,x,y)$ for the Laplacian in a ball. The result accurately describes the exponential behaviour of the kernel for small times and significantly improves the qualitatively…

We estimate the heat kernel of the smooth open set for the isotropic unimodal pure-jump L\'evy process with infinite L\'evy measure and weakly scaling L\'evy-Kchintchine exponent.

We consider the symmetric non-local Dirichlet form $(E, F)$ given by \[ E (f,f)=\int_{R^d} \int_{R^d} (f(y)-f(x))^2 J(x,y) dx dy \] with $F$ the closure of the set of $C^1$ functions on $R^d$ with compact support with respect to $E_1$,…

Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…

In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations, we give a necessary and sufficient condition on the stability of global two-sided…