Related papers: Absolutely continuous spectrum for multi-type Galt…
We provide a complete picture of the local convergence of critical or subcritical Galton-Watson tree conditioned on having a large number of individuals with out-degree in a given set. The generic case, where the limit is a random tree with…
In this paper we show that the spectrum of the Q-codegree of a d-dimensional lattice polytope is finite above any positive threshold in the class of lattice polytopes with \alpha-canonical normal fan for any fixed \alpha>0. For \alpha=1/r…
We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution on a space of trees is said to be self-similar if it is invariant with respect to the operation of pruning, which cuts…
In this paper, for d > 2, we prove the absolute continuity of the spectrum of a d-dimensional periodic Dirac operator with some discontinuous magnetic and electric potentials. In particular, for d = 3, electric potentials from Zygmund…
We discuss a functional model for multi--diagonal selfadjoint operators with almost periodic coefficients that generalizes the well known model for finite band Jacobi matrices. It give us an opportunity to construct examples of almost…
Dilworth's theorem. Every finite distributive lattice $D$ can be represented as the congruence lattice of a finite lattice $L$. We want: Every finite distributive lattice $D$ can be represented as the congruence lattice of a nice finite…
We consider the random conductance model, where the underlying graph is an infinite supercritical Galton--Watson tree, the conductances are independent but their distribution may depend on the degree of the incident vertices. We prove that,…
We consider Schr\"odinger operators $H=-\Delta+V({\mathbf x})$ in ${\mathbb R}^d$, $d\geq2$, with quasi-periodic potentials $V({\mathbf x})$. We prove that the absolutely continuous spectrum of a generic $H$ contains a semi-axis…
We formulate and prove the existence and uniqueness of the generalized Fourier transform associated with the absolutely continuous part of an arbitrary selfadjoint operator on a separable Hilbert space. To this end we develop a novel method…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
We investigate Kesten-Stigum-like results for multi-type Galton-Watson processes with a countable number of types in a general setting, allowing us in particular to consider processes with an infinite total population at each generation.…
We use the Mass Transport Principle to analyze the local recursion governing the resolvent $(A-z)^{-1}$ of the adjacency operator of unimodular random trees. In the limit where the complex parameter $z$ approaches a given location $\lambda$…
We consider conditioned Galton-Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe…
Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose…
We give an elementary proof of an efficient version of the Wagner's theorem on almost invariant subspaces and deduce some consequences in the context of Galois extensions.
We consider a new IDLA - particle system model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. We prove that almost surely all trees are finite.
Matching of the quasi parton distribution functions between continuum and lattice is addressed using lattice perturbation theory specifically with Wilson-type fermions. The matching is done for nonlocal quark bilinear operators with a…
In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…
Given a Galton-Watson process conditioned to have total progeny equal to $n$, we study the asymptotic probability that this conditioned Galton-Watson process has distance to the border bigger or equal than $k$, as the number of nodes $n…
We introduce a comprehensive framework for subordinacy theory applicable to long-range operators on $\ell^2(\mathbb Z)$, bridging dynamical systems and spectral analysis. For finite-range operators, we establish a correspondence between the…