22 citations · 105 across the 26 of their papers we have counts for
28 papers
A weak Hellinger inequality for noisy Boolean channels
Polona Durcik, Marco Fraccaroli, Joris Roos
A weak form of the Hellinger conjecture of Anantharam, Bogdanov, Chakrabarti, Jayram, and Nair for the binary symmetric channel is proved: dictator functions maximize Hellinger …
A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
Floris van Doorn, Polona Durcik, Joris Roos +2
This blueprint serves as a companion to a forthcoming, shorter traditional mathematical paper. The purpose of this blueprint is two-fold: first, it has served as the foundation for…
The shifted bilinear Hilbert transform
Lars Becker, Polona Durcik
We prove estimates for the shifted bilinear Hilbert transform, with a polylogarithmic bound in the size of the shift. As applications, we obtain -variation estimates for b…
Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos +1
A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent . This follows up on previous work, where such bounds were established for n…
On trilinear singular Brascamp-Lieb integrals
Lars Becker, Polona Durcik, Fred Yu-Hsiang Lin
We classify all trilinear singular Brascamp-Lieb forms, completing the classification in the two dimensional case by Demeter and Thiele in arXiv:0803.1268. We use known results in…
Sharp isoperimetric inequalities on the Hamming cube near the critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos
An isoperimetric inequality on the Hamming cube for exponents is proved, achieving equality on any subcube. This was previously known for $β\ge \log_2(3/2)\approx 0.…
Dimension-free estimates for low degree functions on the Hamming cube
Komla Domelevo, Polona Durcik, Valentia Fragkiadaki +4
The main result of this paper are dimension-free inequalities, , for low degree scalar-valued functions on the Hamming cube. More precisely, for any $\vare…
Norm-variation of triple ergodic averages for commuting transformations
Polona Durcik, Lenka Slavíková, Christoph Thiele
We prove an -variation estimate, , in the norm for ergodic averages with respect to three commuting transformations. It is not known whether such estimates hold for all $r\…
A strong-type Furstenberg-Sárközy theorem for sets of positive measure
Polona Durcik, Vjekoslav Kovač, Mario Stipčić
For every , we prove that a positive measure subset of the unit square contains a point such that nontrivially intersects curves $y-y_…
A new proof of an inequality of Bourgain
Polona Durcik, Joris Roos
The purpose of this short note is to demonstrate how some techniques from additive combinatorics recently developed by Peluse and Peluse-Prendiville can be applied to give an alter…
Quantitative bounds for product of simplices in subsets of the unit cube
Polona Durcik, Mario Stipčić
For each , let and let be a set of vertices of a non-degenerate simplex of points in . If $A\subseteq [0,1]^{k_1+1}\tim…
Local bounds for singular Brascamp-Lieb forms with cubical structure
Polona Durcik, Lenka Slavíková, Christoph Thiele
We prove a range of bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expa…
An uncountable ergodic Roth theorem and applications
Polona Durcik, Rachel Greenfeld, Annina Iseli +2
We establish an uncountable amenable ergodic Roth theorem, in which the acting group is not assumed to be countable and the space need not be separable. This generalizes a previous…
Pointwise convergence of certain continuous-time double ergodic averages
Michael Christ, Polona Durcik, Vjekoslav Kovač +1
We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting -actions, coming from a single jointly measurable measure-preserving $\mat…
Trilinear smoothing inequalities and a variant of the triangular Hilbert transform
Michael Christ, Polona Durcik, Joris Roos
Lebesgue space inequalities are proved for a variant of the triangular Hilbert transform involving curvature. The analysis relies on a crucial trilinear smoothing inequality develo…
Boundedness of some multi-parameter fiber-wise multiplier operators
Frédéric Bernicot, Polona Durcik
We prove estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimate…
A Szemerédi-type theorem for subsets of the unit cube
Polona Durcik, Vjekoslav Kovač
We investigate gaps of -term arithmetic progressions inside a positive measure subset of the unit cube . If lengths of their gaps are…
Directional maximal function along the primes
Laura Cladek, Polona Durcik, Ben Krause +1
We study a two-dimensional discrete directional maximal operator along the set of the prime numbers. We show existence of a set of vectors, which are lattice points in a sufficient…
Singular Brascamp-Lieb: a survey
Polona Durcik, Christoph Thiele
We present an overview of results on multi-linear singular integrals in the broader context of Brascamp-Lieb inequalities. This elaborates a lecture given at the inspiring conferen…
Norm-variation of cubic ergodic averages
Polona Durcik, Kristina Ana Škreb
We prove a quantitative result on norm convergence of cubic ergodic averages with respect to commuting measure-preserving transformations. We use harmonic analysis techni…
Averages of simplex Hilbert transforms
Polona Durcik, Joris Roos
We study a multilinear singular integral obtained by taking averages of simplex Hilbert transforms. This multilinear form is also closely related to Calderón commutators and the tw…
Boxes, extended boxes, and sets of positive upper density in the Euclidean space
Polona Durcik, Vjekoslav Kovač
We prove that sets with positive upper Banach density in sufficiently large dimensions contain congruent copies of all sufficiently large dilates of three specific higher-dimension…
Singular Brascamp-Lieb inequalities with cubical structure
Polona Durcik, Christoph Thiele
We prove a singular Brascamp-Lieb inequality, stated in Theorem 1, with a large group of involutive symmetries.
On side lengths of corners in positive density subsets of the Euclidean space
Polona Durcik, Vjekoslav Kovač, Luka Rimanić
We generalize a result by Cook, Magyar, and Pramanik [3] on three-term arithmetic progressions in subsets of to corners in subsets of $\mathbb{R}^d\times\mathbb{R}^d…