" This volume contains the expanded lecture notes of courses taught at the Emile Borel
Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent …

Estimates of heat kernels on Riemannian manifolds Page 154 Estimates of heat kernels on
Riemannian manifolds Alexander Grigor'yan Imperial College London SW7 2BZ England email …

In this paper, we investigate the spectral and the scattering theory of Schrödinger operators
acting on perturbed periodic discrete graphs. The perturbations considered are of two types …

We propose a twisted Szegedy walk for estimating the limit behavior of a discrete-time
quantum walk on a crystal lattice, an infinite abelian covering graph, whose notion was …

We study the spectral properties of Schrödinger operators on perturbed lattices. We shall
prove the non-existence or the discreteness of embedded eigenvalues, the limiting …

We discuss long time asymptotic behaviors of the heat kernel on a non-compact
Riemannian manifold which admits a discontinuous free action of an abelian isometry group …

We consider the Laplacian on a periodic metric graph and obtain its decomposition into a
direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and …

Jacobian Tori Associated with a Finite Graph and Its Abelian Covering Graphs Page 1 Advances
in Applied Mathematics 24, 89–110 (2000) doi:10.1006/aama.1999.0672, available online at …

In this paper we study the spectral structure of the discrete Laplacian on an infinite graph.
We show that, for a finite graph including a certain kind of a family of cycles, the spectrum of …

We discuss a large deviation property of a periodic random walk on a crystal lattice in view
of geometry, and relate it to a rational convex polyhedron in the first homology group of a …