Related papers: The heat semigroup on configuration spaces
Let $\Gamma$ be a finitely generated discrete group acting properly and cocompactly on a smooth manifold M. By employing heat-kernel techniques we prove a geometric formula for the pairing of the index class associated to a…
By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an $r$-dimensional parametric family of optimal geodesics. We apply these results to the…
In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) L\'evy processes on half spaces for all $t>0$. These L\'evy processes may…
We study the thermodynamic properties of the hot gas in a sample of groups in the 0.012-0.024 redshift range, using XMM-Newton observations. We present measurements of temperature, entropy, pressure and iron abundance. Non-parametric fits…
Stochastic incompleteness of a Riemannian manifold $M$ amounts to the nonconservation of probability for the heat semigroup on $M$. We show that this property is equivalent to the existence of nonnegative, nontrivial, bounded (sub)solutions…
We describe a symplectic approach towards thermodynamics in which thermodynamic transformations are described by (symplectic) Hamiltonian dynamics. Upon identifying the spaces of equilibrium states with Lagrangian submanifolds of a…
Parallel to $\widetilde{\mathrm{SL}(2,\mathbb{R})}$-geometry fibering over the hyperbolic plane, we construct a geometry fibering over the Siegel upper half-space $\mathrm{Sp}(2n,\mathbb{R})\curvearrowright {\mathfrak{H}}_n$, and provide a…
We find necessary and sufficient conditions for a finite $K$-bi-invariant measure on a compact Gelfand pair $(G, K)$ to have a square-integrable density. For convolution semigroups, this is equivalent to having a continuous density in…
By introducing the concept of \emph{Kato control pairs} for a given Riemannian minimal heat kernel, we prove that on every Riemannian manifold $(M,g)$ the Kato class $\mathcal{K}(M,g)$ has a subspace of the form $\mathsf{L}^q(M,d\varrho)$,…
This paper studies Hamiltonian circle actions, i.e. circle subgroups of the group Ham(M,\om) of Hamiltonian symplectomorphisms of a closed symplectic manifold (M,\om). Our main tool is the Seidel representation of \pi_1(\Ham(M,\om)) in the…
A self-adjoint operator is constructed on the $L_2$-functions on the $K$-rational points $X(K)$ of a Mumford curve $X$ defined over a non-archimedean local field $K$. It generates a Feller semi-group, and the corresponding heat equation…
By using Hsu's multiplicative functional for the Neumann heat equation, a natural damped gradient operator is defined for the reflecting Brownian motion on compact manifolds with boundary. This operator is linked to quasi-invariant flows in…
In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional maximum volume growth assumption. Following Y. Ding's original…
We study the thermodynamics of the one-dimensional extended Hubbard model at half-filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be…
An attempt toward the operational formulation of quantum thermodynamics is made by employing the recently proposed operations forming positive operator-valued measures for generating thermodynamic processes. The quantity of heat as well as…
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…
Following Boalch-Yamakawa and Meinrenken, we consider a certain class of moduli spaces on bordered surfaces from a quasi-Hamiltonian perspective. For a given Lie group $G$, these character varieties parametrize flat $G$-connections on…
In this paper we use the heat equation in a group of Heisenberg type $\mathbb{G}$ to provide a unified treatment of the two very different extension problems for the time independent pseudo-differential operators $\mathscr L^s$ and…
A theoretical framework for sesquilinear forms defined on the direct sum of Hilbert spaces is developed in the first part. Conditions for the boundedness, ellipticity and coercivity of the sesquilinear form are proved. A criterion of E.-M.…
We construct noncommutative `Riemannian manifold' structures on dual quasitriangular Hopf algebras such as $C_q[SU_2]$ with its standard bicovariant differential calculus, using the quantum frame bundle formalism introduced previously. The…