Related papers: Fractality of wave functions on a Cayley tree: Dif…
This article extends a strong averaging principle for L\'evy diffusions which live on the leaves of a foliated manifold subject to small transversal L\'evy type perturbation to the case of non-compact leaves. The main result states that the…
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The…
Attached to both Yang-Mills and General Relativity about Minkowski spacetime are distinguished gauge independent objects known as the on-shell tree scattering amplitudes. We reinterpret and rigorously construct them as $L_\infty$ minimal…
We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated…
We introduce an alternative coordinate system based on derivative polar and spherical coordinate functions and construct a root-to-canopy analytic formulation for tree fractals. We develop smooth tree fractals and demonstrate the…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
The distribution function of local amplitudes of single-particle states in disordered conductors is calculated on the basis of the supersymmetric $\sigma$-model approach using a saddle-point solution of its reduced version. Although the…
We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…
We exhibit a remarkable equivalence between the dynamics of an intermittent nonlinear map and the electronic transport properties (obtained via the scattering matrix) of a crystal defined on a double Cayley tree. This strict analogy reveals…
The free propagation of acoustic plane waves through cellular periodic materials is generally accompanied by a flow of mechanical energy across the adjacent cells. The paper focuses on the energy transport related to dispersive waves…
McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large…
Propagation of a localised wave function of a massive scalar field is investigated in its rest frame. The complete orthogonal Hermite-Gauss basis is presented, and the Gouy phase and Rayleigh scale notions are adapted. The leading and…
Waves propagating through weakly disordered smooth linear media undergo a universal phenomenon called branched flow. Branched flow has been observed and studied experimentally in various systems by considering coherent waves. Recent…
We deduce from a theorem of Dvorak--Norin that the separation and treewidth profiles of graphs are asymptotically equivalent, resolving a question of Huang--Hume--Kelly--Lam. As an application, we calculate the separation profiles of Cayley…
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially…
A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a flux of energy from the…
We study a linear-fractional Bienaym\'e-Galton-Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads…
The aim of this paper is twofold. First, we study eigenvalues and eigenvectors of the adjacency matrix of a bond percolation graph when the base graph is finite and well approximated locally by an infinite regular graph. We relate…