Related papers: Minimality of interval exchange transformations wi…
Shift spaces with the specification property are intrinsically ergodic, i.e. they have a unique measure of maximal entropy. This can fail for shifts with the weaker almost specification property. We define a new property called one-sided…
In this article, we present a characterization of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of finite points on open Riemann surfaces. As an application, we give a characterization of the…
Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In…
A sharp bound on the number of invariant components of an interval exchange transformation is provided. More precisely, it is proved that the number of periodic components n_per and the number of minimal components n_min of an interval…
In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (e_k) is said to be subsequentially minimal if for every normalized block basis (x_k) of (e_k), there is a…
Modifications of General Relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein's theory by adding solely nondynamical fields. With the minimal…
We study the ergodic properties of compositions of interval exchange transformations and rotations. We show that for any interval exchange transformation T, there is a full measure set of \alpha in [0, 1) so that T composed with R_{\alpha}…
There is a natural connection between the class of diffusions, and a certain class of solutions to the Skorokhod Embedding Problem (SEP). We show that the important concept of minimality in the SEP leads to the new and useful concept of a…
We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of…
We prove that a rank one transformation satisfying a condition called restricted growth is a mixing transformation if and only if the spacer sequence for the transformation is uniformly ergodic. Uniform ergodicity is a generalization of the…
Lower bounds on Hilbert-Samuel multiplicity are known for several types of commutative noetherian local rings, and rings with multiplicities which achieve these lower bounds are said to have minimal multiplicity. The first part of this…
We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theorems of Cubides Kovacsics and Delon on C-minimal fields.…
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch provide a subclass of linear involutions. We call such linear involutions…
We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…
Exchangeability -- in which the distribution of an infinite sequence is invariant to reorderings of its elements -- implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical…
We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…
In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the…
We give a sufficient condition for the ergodicity of the Lebesgue measure for an iterated function system of diffeomorphisms. This is done via the induced iterated function system on the space of continuum (which is called hyper-space). We…
A criterion of joint ergodicity of several sequences of transformations of a probability measure space $X$ of the form $T_{i}^{\phi_{i}(n)}$ is given for the case where $T_{i}$ are commuting measure preserving transformations of $X$ and…
The existence of a spectral gap above the ground state has far-reaching consequences for the low-energy physics of a quantum many-body system. A recent work of Movassagh [R. Movassagh, PRL 119 (2017), 220504] shows that a spatially random…