23 citations · 99 across the 21 of their papers we have counts for
22 papers
Failure of entropic selection for diagonal matrix completion in deep linear networks
Rodrigo Treviño
We study the free-energy gradient flow associated with the depth- deep linear network on the space of invertible real matrices. The loss observes only the diagonal,…
Non-local Dirichlet forms, Gibbs measures, and a cohomological Dirichlet principle for Cantor sets
Rodrigo Treviño
In this paper I study properties of the generators of non-local Dirichlet forms on ultrametric spaces which are the path space of simple stationary…
On transversal Hölder regularity for flat Wieler solenoids
Rodrigo Treviño
This paper studies various aspects of inverse limits of locally expanding affine linear maps on flat branched manifolds, which I call flat Wieler solenoids. Among the aspects studi…
Bratteli diagrams, translation flows and their -algebras
Ian F. Putnam, Rodrigo Treviño
In [LT16], Kathryn Lindsey and the second author constructed a translation surface from a bi-infinite Bratteli diagram. We continue an investigation into these surfaces. The constr…
Aperiodic and linearly repetitive Lorentz gases of finite horizon are not exponentially mixing
Rodrigo Treviño, Agnieszka Zelerowicz
We prove that aperiodic and linearly repetitive Lorentz gases with finite horizon are not mixing with exponential or stretched exponential speed in any dimension for any class of H…
Spectral cocycle for substitution tilings
Boris Solomyak, Rodrigo Treviño
The construction of spectral cocycle from the case of 1-dimensional substitution flows by Bufetov-Solomyak [arXiv:1802.04783] is extended to the setting of pseudo-self-similar tili…
Statistical properties of Lorentz gases on aperiodic tilings, Part 1
Rodrigo Treviño, Agnieszka Zelerowicz
We consider the Lorentz gas model of category A (that is, with no corners and of finite horizon) on aperiodic repetitive tilings of of finite local complexity. We sh…
Quantitative weak mixing for random substitution tilings
Rodrigo Treviño
For compatible substitution rules on prototiles , consider tilings and tiling spaces constructed by applying the different substitution rules at random. Thes…
Tilings and traces
Rodrigo Treviño
This paper deals with (globally) random substitutions on a finite set of prototiles. Using renormalization tools applied to objects from operator algebras we establish upper and lo…
Random Substitution Tilings and Deviation Phenomena
Scott Schmieding, Rodrigo Treviño
Suppose a set of prototiles allows different substitution rules. In this paper we study tilings of constructed from random application of the substitution rules.…
Canonical diffusions on the pattern spaces of aperiodic Delone sets
Patricia Alonso-Ruiz, Michael Hinz, Alexander Teplyaev +1
We consider pattern spaces of aperiodic and repetitive Delone sets of finite local complexity. These spaces are compact metric spaces and constitute a special class of foliated spa…
Equilibrium configurations for generalized Frenkel-Kontorova models on quasicrystals
Rodrigo Treviño
I study classes of generalized Frenkel-Kontorova models whose potentials are given by almost-periodic functions which are closely related to aperiodic Delone sets of finite local c…
Traces of random operators associated with self-affine Delone sets and Shubin's formula
Scott Schmieding, Rodrigo Treviño
We study operators defined on a Hilbert space defined by a self-affine Delone set and show that the usual trace of a restriction of the operator to finite-dimensional subspaces…
Flat surfaces, Bratteli diagrams, and unique ergodicity à la Masur
Rodrigo Treviño
Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the re…
Logarithmic laws and unique ergodicity
Jon Chaika, Rodrigo Treviño
We show that Masur's logarithmic law of geodesics in the moduli space of translation surfaces does not imply unique ergodicity of the translation flow, but that a similar law invol…
Self affine Delone sets and deviation phenomena
Scott Schmieding, Rodrigo Treviño
We study the growth of norms of ergodic integrals for the translation action on spaces coming from expansive, self-affine Delone sets. The linear map giving the self-affinity induc…
Indiscriminate covers of infinite translation surfaces are innocent, not devious
W. Patrick Hooper, Rodrigo Treviño
We consider the interaction between passing to finite covers and ergodic properties of the straight-line flow on finite area translation surfaces with infinite topological type. In…
Diophantine approximations for translation surfaces and planar resonant sets
Luca Marchese, Rodrigo Treviño, Steffen Weil
We consider Teichmüller geodesics in strata of translation surfaces. We prove lower and upper bounds for the Hausdorff dimension of the set of parameters generating a geodesic boun…
Flat surface models of ergodic systems
Kathryn Lindsey, Rodrigo Treviño
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possi…
On the Ergodicity of Flat Surfaces of Finite Area
Rodrigo Treviño
We prove some ergodic theorems for flat surfaces of finite area. The first result concerns such surfaces whose Teichmuller orbits are recurrent to a compact subset of $SL(2;R)/SL(S…
On the Non-Uniform Hyperbolicity of the Kontsevich-Zorich Cocycle for Quadratic Differentials
Rodrigo Treviño
We prove the non-uniform hyperbolicity of the Kontsevich-Zorich cocycle for a measure supported on abelian differentials which come from non-orientable quadratic differentials thro…
Efficient automation of index pairs in computational Conley index theory
Rafael M. Frongillo, Rodrigo Treviño
We present new methods of automating the construction of index pairs, essential ingredients of discrete Conley index theory. These new algorithms are further steps in the direction…