Related papers: Non-Weyl Resonance Asymptotics for Quantum Graphs

For a compact Riemannian manifold $M^{n+1}$ acted isometrically on by a compact Lie group $G$ with cohomogeneity ${\rm Cohom}(G)\geq 2$, we show the Weyl asymptotic law for the $G$-equivariant volume spectrum. As an application, we show in…

In this note, we study non-transitive graphs and prove a number of results when they satisfy a coarse version of transitivity. Also, for each finitely generated group $G$, we produce continuum many pairwise non-quasi-isometric regular…

We describe irreducible representations, coherent states and star-products for algebras of integrals of motions (symmetries) of two-dimensional resonance oscillators. We demonstrate how the quantum geometry (quantum K\"ahler form, metric,…

In this paper we consider the geometric behavior near infinity of some Einstein manifolds $(X^n, g)$ with Weyl curvature belonging to a certain $L^p$ space. Namely, we show that if $(X^n, g)$, $n \geq 7$, admits an essential set and has its…

A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity…

We prove that a graph G is asymptotically isomorphic to the ray if and only if G is uniformly spherically bounded and is of bounded local degrees. This problem arouse in combinatorics and was posed in [3] (Problem 10.1).

We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincar\'e metrics, this leads to a natural…

We study the asymptotic distribution of resonances for scattering by compactly supported potentials in hyperbolic space. We first establish an upper bound for the resonance counting function that depends only on the dimension and the…

We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower and upper estimates for minimal partition energies in…

For a two-dimensional canonical system $y'(t)=zJH(t)y(t)$ on an interval $(0,L)$ with $0<L\le\infty$ whose Hamiltonian $H$ is a.e.\ positive semidefinite, denote by $q_H$ its Weyl coefficient. De~Branges' inverse spectral theorem states…

We demonstrate how resonances in a quantum graph consisting of a compact core and semi-infinite leads can be identified from the eigenvalue behavior of the cut-off system.

We consider the spectral behavior and noncommutative geometry of commutators $[P,f]$, where $P$ is an operator of order $0$ with geometric origin and $f$ a multiplication operator by a function. When $f$ is H\"{o}lder continuous, the…

We study the spectral asymptotics of wave equations on certain compact spacetimes where some variant of the Weyl asymptotic law is valid. The simplest example is the spacetime $S^1 \times S^2$. For the Laplacian on $S^1 \times S^2$ the Weyl…

We consider a simple model of an open partially expanding map. Its trapped set K in phase space is a fractal set. We first show that there is a well defined discrete spectrum of Ruelle resonances which describes the asymptotics of…

Let G be a finitely presented group, and G' its commutator subgroup. Let C be the Cayley graph of G' with all commutators in G as generators. Then C is large scale simply connected. Furthermore, if G is a torsion-free nonelementary…

We consider circulant graphs having $p$ vertices, with $p$ prime. To any such graph we associate a certain number $k$, that we call type of the graph. We prove that for $p>>k$ the graph has no quantum symmetry, in the sense that the quantum…

We examine the asymptotics of the spectral counting function of a compact Riemannian manifold by V.G.~Avakumovic \cite{Avakumovic} and L.~H\"ormander \cite{Hormander-eigen} and show that for the scale of orthogonal and unitary groups ${\bf…

Let $G$ be a compact Lie group, $N\geq 1$ and $L>0$. The random geometric graph on $G$ is the random graph $\Gamma(N,L)$ whose vertices are $N$ random points $g_1,\ldots,g_N$ chosen under the Haar measure of $G$, and whose edges are the…

We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we…

We prove a Weyl asymptotics $N(r) = c r^d + {\mathcal O}_{\epsilon}(r^{d - \kappa + \epsilon})$, $\forall\, 0< \epsilon \ll 1$, for the counting function $N(r) = \sharp\{\lambda_j \in {\mathbb C} \setminus \{0\}:\: |\lambda_j| \leq r^2\}$,…