We consider the quantum graph Hamiltonian on square lattice in Euclidean space, and we show that spectrum of converges to corresponding Schr\"odinger operator space continuum limit, eigenfunctions eigenprojections also converge some sense. employ discrete as intermediate operator, use a recent result by second third author limit operator.

Suppose X is a multivariate diffusion process that observed discretely in time. At each observation time, transformation of the state with noise. The smoothing problem consists recovering path process, consistent observations. We derive novel Markov Chain Monte Carlo algorithm to sample from exact distribution. resulting called Backward Filtering Forward Guiding (BFFG) algorithm. extend include...

We present cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging measures are strongly almost periodic. The corresponding dynamical systems are compact groups and homomorphic images of the underlying torus. In particular, they are strictly ergodic with pure point spectrum and continuous eigenfunctions. Their diffraction can be calcu...