Leonidas Daskalakis

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math.DS2025

Pointwise convergence of ergodic averages along quadratic bracket polynomials

Leonidas Daskalakis

We establish a pointwise convergence result for ergodic averages modeled along orbits of the form $(n ⌊ n k ⌋)_{n \in N}$ , where $k$ is an arbitrary positive…

math.DS2025

Ergodic theorems for bilinear averages, Roth's Theorem and Corners along fractional powers

Leonidas Daskalakis

We prove that for every $c \in (1, 23/22)$ , every probability space $(X, B, μ)$ equipped with two commuting measure-preserving transformations $T, S : X \to X$ and every $f,…

math.DS2025

Pointwise ergodic theorems for non-conventional bilinear averages along $(⌊ n^{c} ⌋, - ⌊ n^{c} ⌋)$

Leonidas Daskalakis

For every $c \in (1, 23/22)$ and every probability dynamical system $(X, B, μ, T)$ we prove that for any $f, g \in L_{μ}^{\infty} (X)$ the bilinear ergodic averages \[ \frac{1}{N}\s…

math.DS2024

Pointwise ergodic theorems along fractional powers of primes

Erik Bahnson, Leonidas Daskalakis, Abbas Dohadwala +1

We establish pointwise convergence for nonconventional ergodic averages taken along $⌊ p^{c} ⌋$ , where $p$ is a prime number and $c \in (1, 4/3)$ on $L^{r}$ , $r \in (1, \infty)$ .…

Pointwise convergence of ergodic averages along quadratic bracket polynomials

Ergodic theorems for bilinear averages, Roth's Theorem and Corners along fractional powers

Pointwise ergodic theorems for non-conventional bilinear averages along (⌊nc⌋,−⌊nc⌋)

Pointwise ergodic theorems along fractional powers of primes

Pointwise ergodic theorems for non-conventional bilinear averages along $(⌊ n^{c} ⌋, - ⌊ n^{c} ⌋)$