Related papers: Effective Mixing and Counting in Bruhat-Tits Trees

We consider the question whether, given a countable system of lattices $(\Gamma_j)_{j \in J}$ in a locally compact abelian group $G$, there exists a sequence of functions $(g_j)_{j \in J}$ such that the resulting generalized shift-invariant…

We extend (scheme-theoretic) Bruhat-Tits theory to quasi-reductive groups i.e. with trivial split unipotent radical over discretely valued henselian non-archimedean fields $K$, whose ring of integers is excellent and residue field is…

Let $\{S_i\}_{i\in \Lambda}$ be a finite contracting affine iterated function system (IFS) on ${\Bbb R}^d$. Let $(\Sigma,\sigma)$ denote the two-sided full shift over the alphabet $\Lambda$, and $\pi:\Sigma\to {\Bbb R}^d$ be the coding map…

Let $G$ be the group $SL(2,\mathbb{R})$, $P\subset G$ be the parabolic subgroup of upper triangular matrices and $\Gamma\subset G$ be a cocompact lattice. A right action of $P$ on $\Gamma\backslash G$ defines an orbit foliation…

A gradient boosting decision tree (GBDT), which aggregates a collection of single weak learners (i.e. decision trees), is widely used for data mining tasks. Because GBDT inherits the good performance from its ensemble essence, much…

For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…

We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by…

Let $\Gamma$ be a group which is virtually free of rank at least 2 and let $\mathcal{F}_{td}(\Gamma)$ be the family of totally disconnected, locally compact groups containing $\Gamma$ as a co-compact lattice. We prove that the values of the…

Let $G$ be a Lie-group and $\Ga\subset G$ a cocompact lattice. For a finite-dimensional, not necessarily unitary representation $\om$ of $\Ga$ we show that the $G$-representation on $L^2(\Ga\bs G,\om)$ admits a complete filtration with…

For a finite simplicial graph $\Gamma$, let $G(\Gamma)$ denote the right-angled Artin group on the complement graph of $\Gamma$. In this article, we introduce the notions of "induced path lifting property" and "semi-induced path lifting…

Models of strong $WW$ scattering in the $s$-wave can be represented in a gauge invariant fashion by defining an effective scalar propagator that represents the strong scattering dynamics. The $\sigma(qq \ra qqWW)$ signal may then be…

We provide new examples of translation actions on locally compact groups with the "local spectral gap property" introduced in \cite{BISG15}. This property has applications to strong ergodicity, the Banach-Ruziewicz problem, orbit…

We describe a new set of public, self-contained, and versatile computational tools for the investigation, manipulation, and evaluation of tree-level amplitudes in pure (super)Yang-Mills and (super)Gravity, $\phi^p$-scalar field theory, and…

In this paper, we explore the properties of zeta functions associated with infinite graphs of groups that arise as quotients of cuspidal tree-lattices, including all non-uniform arithmetic quotients of the tree of rank one Lie groups over…

We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant extension known as '$\Gamma$-species' which incorporates data about 'structural' group actions). This culminates…

Let $G$ be a large group acting on a biregular tree $T$ and $\Gamma \leq G$ a geometrically finite lattice. In an earlier work, the authors classified orbit closures of the action of the horospherical subgroups on $G/\Gamma$. In this…

Tree-shaped graphical models are widely used for their tractability. However, they unfortunately lack expressive power as they require committing to a particular sparse dependency structure. We propose a novel class of generative models…

For a group $\Gamma$, a $\Gamma$-labelled graph is an undirected graph $G$ where every orientation of an edge is assigned an element of $\Gamma$ so that opposite orientations of the same edge are assigned inverse elements. A path in $G$ is…

Given a connected semisimple Lie group $G$ and an arithmetic subgroup $\Gamma$, it is well-known that each irreducible representation $\pi$ of $G$ occurs in the discrete spectrum $L^2_{\text{disc}}(\Gamma\backslash G)$ of…

We define $G$-cospectrality of two $G$-gain graphs $(\Gamma,\psi)$ and $(\Gamma',\psi')$, proving that it is a switching isomorphism invariant. When $G$ is a finite group, we prove that $G$-cospectrality is equivalent to cospectrality with…