Related papers: Interval exchanges, admissibility and branching Ra…
We study the dynamics of renormalisation of an interval exchange transformation which features exact scaling (the cubic Arnoux-Yoccoz model). Using a symbolic space that describes both dynamics and scaling, we characterize the periodic…
We present the first explicit example of an interval exchange transformation with flips (FIET) possessing three distinct invariant ergodic measures. The proof is based on a generalization of M. Keane's method, using the Rauzy induction…
The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset, describing its structural, characterizing, and enumerative properties.
We describe a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point valued probabilities. We derive the procedures for node removal (corresponding to conditional expectation) and arc…
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…
Generalizing a result of MacDonald we give necessary and sufficient conditions for an arbitrary subshift to embed into an irreducible sofic shift factoring through a given cover by an irreducible subshift of finite type (SFT). We obtain…
We discuss discrete one-dimensional Schr\"odinger operators whose potentials are generated by an invertible ergodic transformation of a compact metric space and a continuous real-valued sampling function. We pay particular attention to the…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which…
Changes in input distribution can induce shifts in the average predictions of machine learning models. Such prediction shifts may impact downstream business outcomes (e.g. a bank's loan approval rate), so understanding their causes can be…
A Sturmian sequence is an infinite nonperiodic string over two letters with minimal subword complexity. In two papers, the first written by Morse and Hedlund in 1940 and the second by Coven and Hedlund in 1973, a surprising correspondence…
We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that ifthetranslates are taken only from a subset of the natural…
Multiplicative invariance is a well-studied property of subsets of the unit interval. The theory in the complex plane is less developed. This paper introduces an analogous definition for multiplicative invariance in the complex plane…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
We study transfer principles for upper bounds of motivic exponential functions and for linear combinations of such functions, directly generalizing the transfer principles from [7] by Cluckers-Loeser and [13, Appendix B] by Shin-Templier…
We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…
In this paper we give necessary and sufficient conditions for a bounded linear operator $T$ to be generalized Drazin-Riesz invertible or generalized Drazin-meromorphic invertible. Also, we study generalized Browder's theorem and generalized…