Related papers: Absolutely Continuous Spectrum for the Anderson Mo…

In this paper, we study additive coalescents. Using their representation as fragmentation processes, we prove that the law of a large class of eternal additive coalescents is absolutely continuous with respect to the law of the standard…

Stanley introduced the concept of chromatic symmetric functions of graphs which extends and refines the notion of chromatic polynomials of graphs, and asked whether trees are determined up to isomorphism by their chromatic symmetric…

We prove absolute continuity of the integrated density of states for frequency-independent analytic perturbations of the non-critical almost Mathieu operator under arithmetic conditions on frequency.

We establish an Expander Mixing Lemma for directed graphs in terms of the eigenvalues of an associated asymmetric transition probability matrix, extending the classical spectral inequality to the asymmetric setting. As an application, we…

A one-channel operator is a self-adjoint operator on $\ell^2(\mathbb{G})$ for some countable set $\mathbb{G}$ with a rank 1 transition structure along the sets of a quasi-spherical partition of $\mathbb{G}$. Jacobi operators are a very…

We present here another proof of Oscar Rojo's theorems about the spectrum of graph Laplacian on certain balanced trees, by taking advantage of the symmetry properties of the trees in question, and looking into the eigenfunctions of…

The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…

We introduce the vertex Seidel energy via the diagonal entries of the absolute Seidel matrix. We establish a spectral formula, compute exact values for several graph families, derive bounds, and present a Coulson-type integral…

In this paper we study the theories of the infinite-branching tree and the $r$-regular tree, and show that both of them are pseudofinite. Moreover, we show that they can be realized by infinite ultraproducts of polynomial exact classes of…

The two components for infinite exchangeability of a sequence of distributions $(P_n)$ are (i) consistency, and (ii) finite exchangeability for each $n$. A consequence of the Aldous-Hoover theorem is that any node-exchangeable,…

We consider the problem of change-point detection in multivariate time-series. The multivariate distribution of the observations is supposed to follow a graphical model, whose graph and parameters are affected by abrupt changes throughout…

Let $d \geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is…

We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams…

We prove the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds with residually finite fundamental groups. In real dimension three, where a result of Hempel ensures that the fundamental group…

For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…

We study the connection of the existence of solutions with certain properties and the spectrum of operators in the framework of regular Dirichlet forms on infinite graphs. In particular we prove a version of the Allegretto-Piepenbrink…

We prove that, in the random stirring model of parameter T on an infinite rooted tree each of whose vertices has at least two offspring, infinite cycles exist almost surely, provided that T is sufficiently high. In the appendices, the bound…

We prove a sharp representation stability result for graph complexes with a distinguished vertex, and prove that the chains realizing this sharp bound pass to non-trivial families of graph homology classes. This result may be interpreted as…

We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra…

We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there…