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Publications associées (8)
On distributional autoregression and iterated transportation
Victor Panaretos, Laya Ghodrati
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of Double-struck capital R. An order-1 autoregressive model in this context is to be understood as a Markov chain, where ...
Hoboken2024Moments of the number of points in a bounded set for number field lattices
Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban
We examine the moments of the number of lattice points in a fixed ball of volume for lattices in Euclidean space which are modules over the ring of integers of a number field . In particular, denoting by the number of roots of unity in , we ...
arXiv2023A decomposition of multicorrelation sequences for commuting transformations along primes
A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer and every there exists such that every subset of ${1, ...
2021A new elementary proof of the Prime Number Theorem
Let denote the number of prime factors of . We show that for any bounded one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...
2021Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...
2020Multiplicative combinatorial properties of return time sets in minimal dynamical systems
We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove t ...
2019A generalization of Kátai's orthogonality criterion with applications
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Kátai's orthogonality cri ...
2019On the Hodge decomposition in $\mathbb{R}^n$
We prove a version of the hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. We also compute the cohomology of . ...
2009