27 citations · 72 across the 15 of their papers we have counts for
21 papers
Higher-order hyperuniformity of random measures
Michael Björklund
We study higher-order hyperuniformity through the large-scale variance of local -point patterns, and write $\HU_k$ for the resulting condition; $\HU_1$ is ordinary hyperuniformi…
Completely Positive Entropy and Fourier Central Limit Theorems for Stationary Random Measures
Michael Björklund
We prove an almost-everywhere Fourier central limit theorem for stationary random measures on $\bR^d$ with local second moments whose translation action is essentially free and has…
Hyperuniform Delone Realizations and Rigidity
Michael Björklund
We prove a measurable realization theorem for hyperuniform Delone point processes. In dimensions \(d\geq2\), for every prescribed \(q\geq1\), every essentially free ergodic p.m.p.\…
Stealthy point processes and lattice induction
Michael Björklund
We prove a realization theorem for stealthy point processes based on lattice induction, together with a converse in dimension one. Every probability-preserving -action…
Hyperuniformity of random measures on Euclidean and hyperbolic spaces
Michael Björklund, Mattias Byléhn
We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we…
A Szemerédi type theorem for sets of positive density in approximate lattices
Michael Björklund, Alexander Fish
An extension of Szemerédi's Theorem is proved for sets of positive density in approximate lattices in general locally compact and second countable abelian groups. As a consequence,…
Simplices in large sets and directional expansion in ergodic actions
Michael Björklund, Alexander Fish
In this paper we study ergodic -actions and investigate expansion properties along cyclic subgroups. We show that under some spectral conditions there are always dire…
Sharp density discrepancy for cut and project sets: An approach via lattice point counting
Henna Koivusalo, Jean Lagacé, Michael Björklund +1
Cut and project sets are obtained by taking an irrational slice of a lattice and projecting it to a lower dimensional subspace, and are fully characterised by the shape of the slic…
Analytic properties of approximate lattices
Michael Björklund, Tobias Hartnick
We introduce a notion of cocycle-induction for strong uniform approximate lattices in locally compact second countable groups and use it to relate (relative) Kazhdan- and Haagerup-…
Aperiodic order and spherical diffraction, II: Translation bounded measures on homogeneous spaces
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we stu…
Approximate lattices
Michael Björklund, Tobias Hartnick
In this article we introduce and study uniform and non-uniform approximate lattices in locally compact second countable (lcsc) groups. These are approximate subgroups (in the sense…
Quantitative multiple mixing
Michael Björklund, Manfred Einsiedler, Alexander Gorodnik
We develop a method for providing quantitative estimates for higher order correlations of group actions. In particular, we establish effective mixing of all orders for actions of s…
Approximate invariance for ergodic actions of amenable groups
Michael Björklund, Alexander Fish
We develop in this paper some general techniques to analyze action sets of small doubling for probability measure-preserving actions of amenable groups. As an application of these…
Aperiodic order and spherical diffraction, I: Auto-correlation of model sets
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally com…
Twisted patterns in large subsets of
Michael Björklund, Kamil Bulinski
Let be a set of positive upper Banach density and let be a finitely generated, strongly irreducible subgroup whose Zar…
Characteristic Polynomial Patterns in Difference Sets of Matrices
Michael Björklund, Alexander Fish
We show that for every subset of positive density in the set of integer square-matrices with zero traces, there exists an integer such that the set of characteristic…
Quasi-state Rigidity for Finite-dimensional Lie Algebras
Michael Björklund, Tobias Hartnick
We say that a Lie algebra $\gfr$ is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending…
Ergodic Theorems for coset spaces
Michael Björklund, Alexander Fish
We study in this paper the validity of the mean ergodic theorem along \emph{left} Følner sequences in a countable amenable group . Although the \emph{weak} ergodic theorem alway…
Plünnecke inequalities for countable abelian groups
Michael Björklund, Alexander Fish
We establish in this paper a new form of Plünnecke-type inequalities for ergodic probability measure-preserving actions of any countable abelian group. Using a correspondence princ…
Product set phenomena for countable groups
MIchael Björklund, Alexander Fish
We develop in this paper general techniques to analyze local combinatorial structures in product sets of two subsets of a countable group which are "large" with respect to certain…
Biharmonic functions on groups and limit theorems for quasimorphisms along random walks
Michael Björklund, Tobias Hartnick
We show for very general classes of measures on locally compact second countable groups that every Borel measurable quasimorphism is at bounded distance from a quasi-biharmonic one…