Related papers: Translate of horospheres and counting problems

Let $\Gamma < G$ be an arithmetic lattice in a noncompact connected semisimple real algebraic group. For many such $G$ of rank at most $2$, in particular $G = \operatorname{SL}_3(\mathbb R)$, we prove effective equidistribution of large…

The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are…

Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for "many" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to…

Zaremba's Conjecture concerns the formation of continued fractions with partial quotients restricted to a given alphabet. In order to answer the numerous questions that arrive from this conjecture, it is best to consider a semi-group, often…

In this paper we study a perturbative approach to the problem of quantization of measures in the plane. Motivated by the fact that, as the number of points tends to infinity, hexagonal lattices are asymptotically optimal from an energetic…

Some mathematical aspects of using the translation group as an internal symmetry group in a gauge field theory are presented and discussed. The traditional manner in which gravitation can be accounted for by the introduction of a global…

This note identifies compact and {\sigma}-compact subsets of probability measures on a class of metric spaces with respect to the weak convergence topology. Moreover, it is shown by an example, that the space of probability measures on a…

A well-known conjecture states that the Whitney numbers of the second kind of a geometric lattice (simple matroid) are logarithmically concave. We show this conjecture to be equivalent to proving an upper bound on the number of new copoints…

Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection…

We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize…

Let $G$ be a regular graph and $H$ a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of $H$ one expects to find in a random subgraph of $G$.

We obtain a series of new results on the problem of irreducibility of commuting varieties associated with symmetric pairs or, in other words, $Z_2$-graded simple Lie algebras. In particular, we present many examples of reducible commuting…

Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences and consider the question when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain…

A connection between representation of compact groups and some invariant ensembles of Hermitian matrices is described. We focus on two types of invariant ensembles which extend the Gaussian and the Laguerre Unitary ensembles. We study them…

Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.

Let $\Gamma$ be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if $\Gamma$ is either non-uniform or is uniform of orthogonal type and dimension at least 9, then $\Gamma$ is bi-interpretable…

A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…

Let $(X,\mathfrak{B},\mu)$ be a Borel probability space. Let $T_n: X\rightarrow X$ be a sequence of continuous transformations on $X$. Let $\nu$ be a probability measure on $X$ such that $\frac{1}{N}\sum_{n=1}^N (T_n)_\ast \nu \rightarrow…

We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…

If Gamma is a nonuniform, irreducible lattice in a semisimple Lie group whose real rank is greater than 1, we show Gamma contains a subgroup that is isomorphic to a nonuniform, irreducible lattice in either SL(3,R), SL(3,C), or a direct…