Related papers: On-diagonal lower estimate of heat kernel on graph…
In this work, we establish a new characterization of sub-Gaussian heat kernel estimates for strongly local regular Dirichlet forms on metric measure spaces. Our formulation is based on the newly introduced cutoff energy condition, which…
Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type…
We prove on-diagonal bounds for the heat kernel of the Dirichlet Laplacian $-\Delta^D_\Omega$ in locally twisted three-dimensional tubes $\Omega$. In particular, we show that for any fixed $x$ the heat kernel decays for large times as…
Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the…
We consider skew extensions of expanding maps by compact Lie groups. For a class of natural invariant measures, we prove an explicit lower bound on the rate of (exponential) mixing involving topological pressure. Proof uses representation…
While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…
We establish heat kernel and gradient estimates for the density of kinetic degenerate Kolmogorov stochastic differentia equations. Our results are established under somehow minimal assumptions that guarantee the SDE is weakly well posed.
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of…
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres.…
Aim of this short note is to show that a dimension-free Harnack inequality on an infinitesimally Hilbertian metric measure space where the heat semigroup admits an integral representation in terms of a kernel is suffcient to deduce a sharp…
We obtain a lower bound on each entry of the principal eigenvector of a non-regular connected graph.
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
In this work, we introduce novel algorithms for label propagation and self-training using fractional heat kernel dynamics with a source term. We motivate the methodology through the classical correspondence of information theory with the…
We demonstrate a relationship between the heat kernel on a finite weighted Abelian Cayley graph and Gaussian functions on lattices. This can be used to prove a new inequality for the heat kernel on such a graph: when $t \leq t'$,…
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…
We introduce a new method that exploits the combination of the Heat Kernel (HK) and Background Field Method to compute gauge-invariant and gauge parameter-independent quantities such as the effective potential, anomalous dimensions, and…
Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the…
In this paper, we study Li-Yau gradient estimates for the solutions $u$ to the heat equation $\partial_tu=\Delta u$ on graphs under the curvature condition $CD(n,-K)$ introduced by Bauer et al. in \cite{BHLLMY}. As applications, we derive…
We consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed, undirected graph. We are motivated by the task of deriving lower bounds for consensus protocols and by the so-called "definitive…
The burning number of a graph was recently introduced by Bonato et al. Although they mention that the burning number generalises naturally to directed graphs, no further research on this has been done. Here, we introduce graph burning for…