Michael Hochman

New results on embeddings of self‐similar sets via renormalization

Amir Algom, Michael Hochman, Meng-Ru Wu

Abstract For self‐similar sets , we obtain new results toward the affine embeddings conjecture of Feng–Huang–Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of have algebraic contraction ratios, and also for arbitrary …

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A threshold for Poisson behavior of non-stationary product measures

Michael Hochman, Nicolò Paviato

Abstract Let $\gamma _{n}= O (\log ^{-c}n)$ and let $\nu $ be the infinite product measure whose n th marginal is Bernoulli $(1/2+\gamma _{n})$ . We show that $c=1/2$ is the threshold, above which $\nu $ -almost every point is simply Poisson …

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On the Dimension of αβ-Sets

Michael Hochman

Abstract We show that the Feng–Xiong lower bound of $1/2$ for the box dimension of $\alpha \beta $-sets is tight. We also study how much of an $\alpha \beta $-orbit “carries the dimension”: deleting an arbitrarily small positive density set of times …

il (code pays fourni par la source)

A threshold for Poisson behavior of non-stationary product measures

Michael Hochman, Nicolò Paviato

Let $γ_{n}= O (\log^{-c}n)$ and let $ν$ be the infinite product measure whose $n$-th marginal is Bernoulli$(1/2+γ_{n})$. We show that $c=1/2$ is the threshold, above which $ν$-almost every point is simply Poisson generic in the sense of Peres-Weiss, and below which this …

On the Analytic Self-maps of Cantor Sets in the Line

Michael Hochman

il (code pays fourni par la source)

Some remarks about self-products and entropy

Michael Hochman

Abstract Let $(X,\mathcal {B},\mu ,T)$ be a probability-preserving system with X compact and T a homeomorphism. We show that if every point in $X\times X$ is two-sided recurrent, then $h_{\mu }(T)=0$ , resolving a problem of Benjamin Weiss, and that if $h_{\mu …

il (code pays fourni par la source)

On the dimension of $αβ$-sets

Michael Hochman

We show that the Feng-Xiong lower bound of $1/2$ for the box dimension of $αβ$-sets is tight. We also study how much of an $αβ$-orbit ``carries the dimension'': deleting an arbitararily small positive density set of times can cause the box dimension …

Preface from the Series Editor

Michael Hochman

When I was a third-year medical student, I asked one of my senior residents—who seemed to be able to quote every medical study in the history of mankind—if he had a list of key studies that have defined the current practice of …

Irreducibility and periodicity in $\mathbb{Z}^{2}$ symbolic systems

Michael Hochman

We show that there exist $\mathbb{Z}^{2}$ symbolic systems that are strongly irreducible and have no (fully) periodic points

Some remarks about self-products and entropy

Michael Hochman

Let $(X,\mathcal{B},μ,T)$ be a probability-preserving system with $X$ compact and $T$ a homeomorphism. We show that if every point in $X\times X$ is two-sided recurrent, then $h_μ(T)=0$, resolving a problem of Benjamin Weiss, and that if $h_μ(T)=\infty$ then every full-measure set in …

On the analytic self-maps of Cantor sets in the line

Michael Hochman

We show that a topological Cantor set in the line has at most countably many real-analytic, onto self-maps.

MDS-195 Characterization of Patients With Co-Occurrent Clonal Myeloid and Plasma Cell Disorders: A Single Center Descriptive Case Series

Michael Hochman, Gloria F. Gerber, Philip Imus, Syed Abbas Ali et autres

us (code pays fourni par la source)