Related papers: Wrapping Brownian motion and heat kernels on compa…
A new equation, rooted in the theory of Brownian motion, is proposed for describing heat conduction by phonons. Though a finite speed of propagation is a built-in feature of the equation, it does not give rise to an inauthentic wave front…
The purpose of this article is to establish regularity and pointwise upper bounds for the (relative) fundamental solution of the heat equation associated to the weighted dbar-operator in $L^2(C^n)$ for a certain class of weights. The…
In this paper, we obtain an explicit formula for the heat kernel on the infinite Cayley graph of the modular group $\operatorname{PSL}_2\mathbb{Z}$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle$. Our approach extends the…
Let $X$ be an abstract orientable not necessarily compact CR manifold of dimension $2n+1$, $n\geq1$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Suppose that condition $Y(q)$ holds at each point of…
We study semigroups generated by two-dimensional relativistic Hamiltonians with magnetic field. In particular, for compactly supported radial magnetic field we show how the long time behaviour of the associated heat kernel depends on the…
This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…
Anisotropic hybrid nanostructures stand out as promising therapeutic agents in photothermal conversion-based treatments. Accordingly, understanding local heat generation mediated by light-to-heat conversion of absorbing multicomponent…
Networks constitute fundamental organizational structures across biological systems, although conventional graph-theoretic analyses capture exclusively pairwise interactions, thereby omitting the intricate higher-order relationships that…
Brownian motion of a heavy charged particle at zero and small (but finite) temperature is studied in presence of finite density. We are primarily interested in the dynamics at (near) zero temperature which is holographically described by…
In this article, we consider the radial Dunkl geometric case $k=1$ corresponding to flat Riemannian symmetric spaces in the complex case and we prove exact estimates for the positive valued Dunkl kernel and for the radial heat kernel. Dans…
This note proposes rapidly convergent computational formulae for evaluating scattering kernels from radiative transfer theory. The approach used here does not rely on Legendre expansions, but rather uses exponentially convergent numerical…
We establish the large-$N$ asymptotic expansion of the (central) trace of the heat kernel on any compact classical group $G_N\subset\mathrm{GL}_N(\mathbb{C})$, which extends a previous result known only for $\mathrm{U}(N)$ \cite{LM2}. It…
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…
The starting point of our analysis is an old idea of writing an eigenfunction expansion for a heat kernel considered in the case of a hypoelliptic heat kernel on a nilpotent Lie group $G$. One of the ingredients of this approach is the…
We construct the fundamental solution (the heat kernel) $p^{\kappa}$ to the equation $\partial_t=\mathcal{L}^{\kappa}$, where under certain assumptions the operator $\mathcal{L}^{\kappa}$ takes one of the following forms, \begin{align*}…
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating…
We use tools from $n$-dimensional Brownian motion in conjunction with the Feynman-Kac formulation of heat diffusion to study nodal geometry on a compact Riemannian manifold $M$. On one hand we extend a theorem of Lieb and prove that any…
We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function itself. We then apply these bounds to…
Using the explicit representations of the Brownian motions on the hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity are easily obtained. We also…
In this paper we study heat kernels associated to a Carnot group $G$, endowed with a family of collapsing left-invariant Riemannian metrics $\sigma_\e$ which converge in the Gromov-Hausdorff sense to a sub-Riemannian structure on $G$ as…