Related papers: Varadhan Asymptotics for the Heat Kernel on Finite…

In this paper, we study the heat kernel associated to the intrinsic sublaplacian on a quaternionic contact manifold considered as a subriemannian manifold. More precisely, we explicitly compute the first two coefficients $c_0$ and $c_1$…

Let $P$ be a second-order, symmetric, and nonnegative elliptic operator with real coefficients defined on noncompact Riemannian manifold $M$, and let $V$ be a real valued function which belongs to the class of {\em small perturbation…

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…

We study the heat trace for both the drifting Laplacian as well as Schr\"odinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term)…

In this paper, we study the asymptotic behavior of the heat kernel with respect to the Witten Laplacian. We introduce the localization and the scaling technique in semi-classical analysis, and study the semi-classical asymptotic behavior of…

We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl…

We consider the Cauchy problem for the generalized Fornberg-Whitham equation with dissipation. This is one of the nonlinear, nonlocal and dispersive-dissipative equations. The main topic of this paper is an asymptotic analysis for the…

We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishing a Varadhan-type formula for non-linear semigroups. We do…

We establish small-time asymptotic expansions for heat kernels of hypoelliptic H\"ormander operators in a neighborhood of the diagonal, generalizing former results obtained in particular by M\'etivier and by Ben Arous. The coefficients of…

We study heat semigroups generated by self-adjoint Laplace operators on metric graphs characterized by the property that the local scattering matrices associated with each vertex of the graph are independent from the spectral parameter. For…

We introduce a generalized Bartholdi zeta function for simple graphs with bounded degree. This zeta function is a generalization of both the Bartholdi zeta function which was introduced by L.~Bartholdi and the Ihara zeta function which was…

In this paper we continue the analysis of spectral problems in the setting of complete manifolds with fibred boundary metrics, also referred to as $\phi$-metrics, as initiated in our previous work. We consider the Hodge Laplacian for a…

We obtain the asymptotics, as $t + |x| \rightarrow \infty$, of the fundamental solution to the heat equation with a compactly supported potential. It is assumed that the corresponding stationary operator has at least one positive…

We approximate the heat kernel $h(x,y,t)$ on a compact connected Riemannian manifold $M$ without boundary uniformly in $(x,y,t)\in M\times M\times [a,b]$, $a>0$, by $n$-fold integrals over $M^n$ of the densities of Brownian bridges.…

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 $-\N^\mu\N_\mu$. Our…

Let $G$ be a compact connected Lie group equipped with a bi-invariant metric. We calculate the asymptotic expansion of the heat kernel of the laplacian on $G$ and the heat trace using Lie algebra methods. The Duflo isomorphism plays a key…

We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel…

Upper and lower bounds on the heat kernel on complete Riemannian manifolds were obtained in a series of pioneering works due to Cheng-Li-Yau, Cheeger-Yau and Li-Yau. However, these estimates do not give a complete picture of the heat kernel…

We prove a variant of the Davies-Gaffney-Grigor'yan Lemma for the continuous time heat kernel on graphs. We use it together with the Li-Yau inequality to obtain strong heat kernel estimates for graphs satisfying the exponential curvature…