Related papers: Heat kernel and Green function estimates on affine…
We present a formulation of a nonequilibrium Green's function method for thermal current in nanojunction atomic systems with nonlinear interactions. This first-principle approach is applied to the calculation of the thermal conductance in…
We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases.…
Optimal pointwise estimates are derived for the biharmonic Green function under Dirichlet boundary conditions in arbitrary $C^{4,\gamma}$-smooth domains. Maximum principles do not exist for fourth order elliptic equations and the Green…
We investigate the full counting statistics of extreme-near-field radiative heat transfer using nonequilibrium Green's function formalism. In the extreme near field, the electron-electron interactions between two metallic bodies dominate…
We describe how to apply the recursive Green's function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several…
An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal…
In this paper we prove a rate of escape theorem and a central limit theorem for isotropic random walks on Fuchsian buildings, giving formulae for the speed and asymptotic variance. In particular, these results apply to random walks induced…
We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of well known two-sided Gaussian heat kernel…
We study the trapping phenomenon of random walks in random environments of i.i.d. random conductances on the bonds of the grid $\mathbb{Z}^d$, the so-called random conductance model. Our main results concern the important model with…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We study the surface elastic response of pure Ni, the random alloy FeNiCr and an average FeNiCr alloy in terms of the surface lattice Green's function. We propose a scheme for computing per-site Green's function and study their per-site…
The green functions for the heat and Laplace equations with dynamical boundary conditions in a ball are studied. First, the green functions of the Laplace equation with a dynamical boundary condition are given, and the properties of related…
The heat kernel on the symmetric space of positive definite Hermitian matrices is used to endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of probability measures depending on a choice of the background…
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the…
We prove diffusive lower bounds on the rate of escape of the random walk on infinite transitive graphs. Similar estimates hold for finite graphs, up to the relaxation time of the walk. Our approach uses nonconstant equivariant harmonic…
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…
Some elementary algebraic points regarding the Green function for a localised flux tube are developed. A calculation of the effective action density is included.
We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…
Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green's function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method.…