Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Distribution of shapes of orthogonal lattices

- M. Einsiedler, Ren'e Ruhr, P. Wirth
- Mathematics
- 10 September 2016

It was recently shown by Aka, Einsiedler and Shapira that if d>2, the set of primitive vectors on large spheres when projected to the d-1-dimensional sphere coupled with the shape of the lattice in… Expand

8- PDF

Effectivity of Uniqueness of the Maximal Entropy Measure on $p$-adic homogeneous spaces

- Ren'e Ruhr
- Mathematics
- 8 December 2014

We consider the dynamical system given by an Ad-diagonalizable element a of the Qp-points G of a unimodular linear algebraic group acting by translation on a finite volume quotient X . Assuming that… Expand

4- PDF

Pressure Inequalities for Gibbs Measures of Countable Markov Shifts

- Ren'e Ruhr
- Mathematics
- 24 December 2020

X = {x = (x0, x1, . . . ) ∈ S0 : txixj = 1} for a countable sets of states S, A = (tij)i,j∈S denotes the transition matrix and T : X → X is the left shift, which we assume to be topologically mixing.… Expand

Effective counting on translation surfaces

- A. Nevo, Ren'e Ruhr, B. Weiss
- Mathematics
- 21 August 2017

We prove an effective version of a celebrated result of Eskin and Masur: for any affine invariant manifold of translation surfaces, almost every translation surface has quadratic growth for the… Expand

5- PDF

Metric Diophantine approximation with congruence conditions

- Erez Nesharim, Ren'e Ruhr, R. Shi
- Mathematics
- 4 February 2019

We prove a version of the Khinchine--Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to the… Expand

1- PDF

Effective counting for discrete lattice orbits in the plane via Eisenstein series

- Claire Burrin, A. Nevo, Ren'e Ruhr, B. Weiss
- Mathematics
- 4 May 2019

We prove effective bounds on the rate in the quadratic growth asymptotics for the orbit of a non-uniform lattice of SL(2,R), acting linearly on the plane. This gives an error bound in the count of… Expand

1- PDF

Counting saddle connections in a homology class modulo $q$

- M. Magee, Ren'e Ruhr, Rodolfo Guti'errez-Romo
- Mathematics
- 1 September 2018

We give effective estimates for the number of saddle connections on a translation surface that have length $\leq L$ and are in a prescribed homology class modulo $q$. Our estimates apply to almost… Expand

2- PDF

A Convexity Criterion for Unique Ergodicity of Interval Exchange Transformations

- Ren'e Ruhr
- Mathematics
- 13 November 2019

There is a meta-conjecture in metric number theory that states that any Diophantine property that holds for generic vectors in R should hold for generic vectors on nondegenerate subvarities, see… Expand

Quantitative Multiple pointwise convergence and effective multiple correlations

- Ren'e Ruhr, R. Shi
- Mathematics
- 30 April 2019

We show that effective $2\ell$-multiple correlations imply quantitative $\ell$-multiple pointwise ergodic theorems. The result has a wide class of applications which include subgroup actions on… Expand

1- PDF

Classification and statistics of cut and project sets

- Ren'e Ruhr, Yotam Smilansky, B. Weiss
- Mathematics
- 24 December 2020

We define Ratner-Marklof-Strömbergsson measures (following [MS14]). These are probability measures supported on cutand-project sets in R pd ě 2q which are invariant and ergodic for the action of the… Expand