Related papers: Martingale and analytic dimensions coincide under …

We characterize Gaussian estimates for transition probability of a discrete time Markov chain in terms of geometric properties of the underlying state space. In particular, we show that the following are equivalent: (1) Two sided Gaussian…

A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified…

The analytic expression obtained in the preceding project for the massless conformal scalar propagator in the Hartle-Hawking vacuum state for small values of the Schwarzschild radial coordinate above $ r = 2M$ is analytically extended into…

We study the pointwise dimension for a new class of projection measures on arbitrary fractal limit sets without separation conditions. We prove that the pointwise dimension exists a.e. for this class of measures associated to equilibrium…

The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the…

Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Laplacian on 1-forms is strongly positive…

We prove a martingale analog of van Schaftingen's theorem and give sharp estimates on the lower Hausdorff dimension of measures in martingale shift invariant spaces. We also provide martingale analogs of trace theorems for Sobolev…

We prove that for a general diffusion process, certain assumptions on its behavior \emph{only within a fixed open subset} of the state space imply the existence and sub-Gaussian type off-diagonal upper bounds of the \emph{global} heat…

We give large-time asymptotic estimates, both in uniform and $L^1$ norms, for solutions of the Dirichlet heat equation in the complement of a bounded open set of $\mathbb{R}^d$ satisfying certain technical assumptions. We always assume that…

This paper proves the strong parabolic Harnack inequality for local weak solutions to the heat equation associated with time-dependent (nonsymmetric) bilinear forms. The underlying metric measure Dirichlet space is assumed to satisfy the…

The Ginibre point process is given by the eigenvalue distribution of a non-hermitian complex Gaussian matrix in the infinite matrix-size limit. This is a determinantal point process (DPP) on the complex plane ${\mathbb{C}}$ in the sense…

In this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on the eigenfunctions of the diffusion operator. Since a Bessel process is non-ergodic and the theory of martingale…

We construct a conservative and strongly local regular symmetric Dirichlet form on the pointed Gromov--Hausdorff limit space and demonstrate the stability of heat kernel estimates under this convergence. Furthermore, we establish the Mosco…

We present a multidimensional extension of Kellerer's theorem on the existence of mimicking Markov martingales for peacocks, a term derived from the French for stochastic processes increasing in convex order. For a continuous-time peacock…

We consider the squared singular values of the product of $M$ standard complex Gaussian matrices. Since the squared singular values form a determinantal point process with a particular Meijer G-function kernel, the gap probabilities are…

Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, our new approach takes into account suitable weighted action functionals…

We prove that in presence of $L^2$ Gaussian estimates, so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.

We introduce the notion of Bartlett spectral measure for isometrically invariant random measures on proper metric commutative spaces. When the underlying Gelfand pair corresponds to a higher-rank, connected, simple matrix Lie group with…

We consider the heat equation on a bounded $C^1$ domain in $\mathbb{R}^n$ with Dirichlet boundary conditions. The primary aim of this paper is to prove that the heat equation is observable from any measurable set with a Hausdorff dimension…

Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal…