Related papers: Heat kernel and Green function estimates on affine…
A Green's function formalism is used to calculate the spectrum of localized modes of an impurity layer implanted within a ferromagnetic thin film. The equations of motion for the Green's functions are determined in the framework of the…
Using the logarithmic capacity, we give quantitative estimates of the Green function, as well as lower bounds of the Bergman kernel for bounded pseudoconvex domains in $\mathbb C^n$ and the Bergman distance for bounded planar domains. In…
It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also shown that Ancona's inequalities extend to R, and…
We have calculated the asymptotics of Green's function of the differential equation of nonlinear diffusion in the microscopic range with strong porosity fluctuations in the problem of flow through irregular packed beds for arbitrary space…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
Motivated by the spectral theory of relativistic atoms, we prove matching upper and lower bounds for the transition density of Hardy perturbations of subordinated Bessel heat kernels. The analysis is based on suitable supermedian functions,…
Accurately predicting nonlinear transient thermal fields in two-dimensional domains is a significant challenge in various engineering fields, where conventional analytical and numerical methods struggle to balance physical fidelity with…
Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic…
We consider random walks on the torus arising from the action of the group of affine transformations. We give a quantitative equidistribution result for this random walk under the assumption that the Zariski closure of the group generated…
We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…
In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of…
Motivated by multi-topology building and city model data, first a lossless representation of multiple $T_0$-topologies on a given finite set by a vertex-edge-weighted graph is given, and the subdominant ultrametric of the associated…
By using various properties of the complete elliptic integrals, we have derived an alternative expression for the gravitational potential of axially symmetric bodies, which is free of singular kernel in contrast with the classical form.…
We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided…
We define the reflection of a random walk at a general barrier and derive, in case the increments are light tailed and have negative mean, a necessary and sufficient criterion for the global maximum of the reflected process to be finite…
The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a…
We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on…
We present a general nonequilibrium Green's function formalism for modeling heat transfer in systems characterized by linear response that establishes the formal algebraic relationships between phonon and radiative conduction, and reveals…
We study the heat kernel and the Green's function on the infinite supercritical percolation cluster in dimension $d \geq 2$ and prove a quantitative homogenization theorem for these functions with an almost optimal rate of convergence.…
We revisit the classic thermodynamic problem of maximum work extraction from two arbitrary sized hot and cold reservoirs, modelled as perfect gases. Assuming ignorance about the extent to which the process has advanced, which implies an…