J. Rosenblatt

activity

20112025

most citedRigidity and Non-recurrence along Sequences

29 citations · 34 across the 13 of their papers we have counts for

collaborators

16 papers

math.DS2025

Absolute and Unconditional Convergence of Series of Ergodic Averages and Lebesgue Derivatives

Bryan Johnson, Joseph Rosenblatt

We consider when there is absolute or unconditional convergence of series of various types of stochastic processes. These processes include differences of averages in ergodic theor…

math.DS2024★ 1 cited

Pointwise Convergence of Sequences of Singular Measures

Andrew Parrish, Joseph Rosenblatt

We investigate the almost everywhere convergence of sequences of convolution operators given by probability measures $μ_{n}$ on $R$ . If this sequence of operators constitutes…

math.DS2024

Fluctuation of ergodic averages and other stochastic processes

Sovanlal Mondal, Joe Rosenblatt, Máté Wierdl

For an ergodic map $T$ and a non-constant, real-valued $f \in L^{1}$ , the ergodic averages $A_{N} f (x) = \frac{1}{N} \sum_{n = 1}^{N} f (T^{n} x)$ converge a.e., but the convergence…

math.DS2023

Moving Averages

Terrence Adams, Joseph Rosenblatt

We consider the convergence of moving averages in the general setting of ergodic theory or stationary ergodic processes. We characterize when there is universal convergence of movi…

math.CA2022

Generation of measures on the torus with good sequences of integers

E. Lesigne, A. Quas, J. Rosenblatt +1

Let $S = (s_{1} < s_{2} < \dots)$ be a strictly increasing sequence of positive integers and denote $e (β) = e^{2 π i β}$ . We say $S$ is good if for every real $α$ the limit $\…

math.CA2022

Asymptotic Directions for the Zero Sets of the Components of an Electrical Field from a Finite Number of Point Charges on the Plane Part II

Tamas Erdelyi, Joseph Rosenblatt, Rebecca Rosenblatt

We study the structure of the zero set of a nontrivial finite point charge electrical field $F = (X, Y)$ in the plane $R^{2}$ . We establish equations satisfied by the possible…

math.CA2022

Almost everywhere convergence for Lebesgue differentiation processes along rectangles

Emma D'Aniello, Anthony Gauvan, Laurent Moonens +1

In this paper, we study Lebesgue differentiation processes along rectangles $R_{k}$ shrinking to the origin in the Euclidean plane, and the question of their almost everywhere conver…

math.DS2022

Directional ergodicity and weak mixing for actions of $R^{d}$ and $Z^{d}$

E. Arthur Robinson, Joseph Rosenblatt, Ayşe A. Şahin

We define notions of direction $L$ ergodicity, weak mixing, and mixing for a measure preserving $Z^{d}$ action $T$ on a Lebesgue probability space $(X, μ)$ , where $L\subseteq\…

math.CA2021

The Zero Set of an Electric Field from a Finite Number of Point Charges

Tamás Erdélyi, Joseph Rosenblatt, Rebecca Rosenblatt

We consider the structure of the zero set in $R^{3}$ of the electric vector field $F = (X, Y, Z)$ from a finite set of point charges. We are most interested in the ca…

math.DS2019★ 3 cited

Existence and Non-existence of Solutions to the Coboundary Equation for Measure Preserving Systems

Terrence Adams, Joseph Rosenblatt

Let $(X, B, μ)$ be a standard probability space. We give new fundamental results determining solutions to the coboundary equation: \begin{eqnarray*} f = g - g \circ T \end{…

math.CA2018

Differentiating Orlicz spaces with rare bases of rectangles

Emma D 'Aniello, Laurent Moonens, Joseph Rosenblatt

In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of re…

math.DS2018

Optimal Quantization via Dynamics

Joseph Rosenblatt, Mrinal Kanti Roychowdhury

Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We con…

math.DS2017

Joint coboundaries

Terry Adams, Joseph Rosenblatt

We ask under what conditions on the function $f$ , and a set of maps $T$ , it is the case that $f$ is a coboundary for some map in $T$ . We also consider for a funct…

math.PR2017

Optimal quantization for piecewise uniform distributions

Joseph Rosenblatt, Mrinal Kanti Roychowdhury

Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, fi…

math.DS2012★ 1 cited

Multivariable averaging on sparse sets

Patrick LaVictoire, Andrew Parrish, Joseph Rosenblatt

Nonstandard ergodic averages can be defined for a measure-preserving action of a group on a probability space, as a natural extension of classical (nonstandard) ergodic averages. W…

math.DS2011★ 29 cited

Rigidity and Non-recurrence along Sequences

V. Bergelson, A. del Junco, M. Lemańczyk +1

Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do n…

Absolute and Unconditional Convergence of Series of Ergodic Averages and Lebesgue Derivatives

Pointwise Convergence of Sequences of Singular Measures

Fluctuation of ergodic averages and other stochastic processes

Moving Averages

Generation of measures on the torus with good sequences of integers

Asymptotic Directions for the Zero Sets of the Components of an Electrical Field from a Finite Number of Point Charges on the Plane Part II

Almost everywhere convergence for Lebesgue differentiation processes along rectangles

Directional ergodicity and weak mixing for actions of Rd and Zd

The Zero Set of an Electric Field from a Finite Number of Point Charges

Existence and Non-existence of Solutions to the Coboundary Equation for Measure Preserving Systems

Differentiating Orlicz spaces with rare bases of rectangles

Optimal Quantization via Dynamics

Joint coboundaries

Optimal quantization for piecewise uniform distributions

Multivariable averaging on sparse sets

Rigidity and Non-recurrence along Sequences

Directional ergodicity and weak mixing for actions of $R^{d}$ and $Z^{d}$