Related papers: Global Heat Kernel Estimate for Relativistic Stabl…
We establish sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying $\RCD(0,N)$ ( equivalently, $\RCD^\ast(0,N)$) condition with $N\in \mathbb{N}\setminus\{1\}$ and having maximum volume…
In this paper we consider the following SDE with distributional drift $b$: $$ {\rm d} X_t=\sigma(X_t){\rm d} B_t+b(X_t){\rm d} t,\ X_0=x\in{\mathbb R}^d, $$ where $\sigma$ is a bounded continuous and uniformly non-degenerate $d\times…
We investigate Sine$_\beta$, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or $\beta$-ensembles, at inverse temperature $\beta>0$. We adopt a…
The heat kernel for the spin-3/2 Rarita-Schwinger gauge field on an arbitrary Ricci flat space-time ($d>2$) is investigated in a family of covariant gauges with one gauge parameter $\alpha$. The $\alpha$-dependent term of the kernel is…
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…
This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not…
We discuss an approach to determine averages of the work, dissipated heat and variation of internal energy of an open quantum system driven by an external classical field. These quantities are measured by coupling the quantum system to a…
For a complex manifold $\Sigma $ with $\mathbb{C}^{\ast }$-action, we define the $m$-th $\mathbb{C}^{\ast }$ Fourier-Dolbeault cohomology group and consider the $m$-index on $\Sigma $. By applying the method of transversal heat kernel…
We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…
The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
We prove sharp estimates on heat kernels and Green functions for subordinate Markov processes with both discrete an continuous time, under relatively weak assumptions about original processes as well as Laplace exponents of subordinators.…
The paper is concerned with constructing pairwise dependence between $m$ random density functions each of which is modeled as a mixture of Dirichlet process model. The key to this is how to create dependencies between random Dirichlet…
By making full use of heat kernel estimates, we establish the integral tests on the zero-one laws of upper and lower bounds for the sample path ranges of symmetric Markov processes. In particular, these results concerning on upper rate…
We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain…
In this paper, we investigate the thermodynamic properties of a set of neutral Dirac particles in the presence of an electromagnetic field in contact with a heat bath for the relativistic and non-relativistic cases. In order to perform the…
In this paper we study the transition densities for a large class of non-symmetric Markov processes whose jumping kernels decay exponentially or subexponentially. We obtain their upper bounds which also decay at the same rate as their…
The aim of this article is to establish two-sided Gaussian bounds for the heat kernels on the unit ball and simplex in $\mathbb{R}^n$, and in particular on the interval, generated by classical differential operators whose eigenfunctions are…
A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For large…
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…