7 papers
Invariant random compacts
Bryna Kra, Scott Schmieding
For a compact metric space with a group acting on it continuously, an invariant random compact is a Borel probability measure on the space of nonempty compact subsets of $X…
A short proof of Erdős's conjecture
Bryna Kra, Joel Moreira, Florian K. Richter +1
We give a short proof of the fact that every set of natural numbers with positive upper Banach density contains the sum of two infinite sets. The approach simplifies earlier existi…
Stable covers of subshifts
Solly Coles, Van Cyr, Bryna Kra +1
Given a dynamical system, a characteristic measure is a Borel probability measure invariant under all of its automorphisms. Frisch and Tamuz asked if every symbolic system supports…
The Density Finite Sums Theorem
Bryna Kra, Joel Moreira, Florian K. Richter +1
For any set of natural numbers with positive upper Banach density and any , we show the existence of an infinite set and a shift such th…
Ergodic averages and the large intersection property along IP sets
Bryna Kra, Or Shalom
We study multiple ergodic averages along IP sets, meaning we restrict iterates in the averages to all finite sums of some infinite sequence of natural numbers. We give criteria for…
Problems on infinite sumset configurations in the integers and beyond
Bryna Kra, Joel Moreira, Florian K. Richter +1
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Buildi…